Papers updated in last 365 days (2580 results)

Last updated:  2023-09-26
Circuit-Succinct Universally-Composable NIZKs with Updatable CRS
Behzad Abdolmaleki, Noemi Glaeser, Sebastian Ramacher, and Daniel Slamanig
Non-interactive zero-knowledge proofs (NIZKs) and in particular succinct NIZK arguments of knowledge (zk-SNARKs) increasingly see real-world adoption in large and complex systems. Many zk-SNARKs require a trusted setup, i.e., a common reference string (CRS), and for practical use it is desirable to reduce the trust in the CRS generation. The latter can be achieved via the notions of subversion or updatable CRS. Another important property when deployed in large systems is the ability to securely compose them to obtain more complex protocols, e.g., via the Universal Composability (UC) framework. Relying on the UC framework allows arbitrary and secure composition of protocols in a modular way. In this work, we investigate whether zk-SNARKs can provide updatability and composability simultaneously. This is a challenging task as the UC framework rules out several natural techniques for such a construction. As our main result, we show that it is indeed possible to achieve these properties in a generic and modular way if we relax the succinctness properties of zk-SNARKs slightly to those of a circuit-succinct NIZK which is not witness-succinct, i.e., by increasing the proof size of the underlying zk-SNARK by the size of the witness $w$. We argue that for various practical applications of zk-SNARKs this overhead is acceptable. Our starting point is the Lamassu framework (ACM CCS'20), which we extend in several directions. Our new generic compiler adds only minimal overhead, which we demonstrate by benchmarking its application to the Sonic proof system (ACM CCS'19).
Last updated:  2023-09-26
Improved Polynomial Secret-Sharing Schemes
Amos Beimel, Oriol Farràs, and Or Lasri
Despite active research on secret-sharing schemes for arbitrary access structures for more than 35 years, we do not understand their share size $-$ the best known upper bound for an arbitrary n-party access structure is $2^{O(n)}$ while the best known lower bound is $\Omega(n/\log(n))$. Consistent with our knowledge, the share size can be anywhere between these bounds. To better understand this question, one can study specific families of secret-sharing schemes. For example, linear secret-sharing schemes, in which the sharing and reconstruction are computed by linear mappings, have been studied in many papers, e.g., it is known that they require shares of size at least $2^{0.5n}$. Secret-sharing schemes in which the sharing and/or reconstruction are computed by low-degree polynomials have been recently studied by Paskin-Cherniavsky and Radune [ITC 2020] and by Beimel, Othman, and Peter [CRYPTO 2021]. It was shown that secret-sharing schemes with sharing and reconstruction computed by polynomials of degree 2 are more efficient than linear schemes (i.e., schemes in which the sharing and reconstruction are computed by polynomials of degree one). Prior to our work, it was not known if using polynomials of higher degree can reduce the share size. We show that this is indeed the case, i.e., we construct secret-sharing schemes with reconstruction by degree-$d$ polynomials, where as the reconstruction degree $d$ increases, the share size for arbitrary access structures decreases. As a step in our construction, we construct conditional disclosure of secrets (CDS) protocols. For example, we construct 2-server CDS protocols for functions $f : [N ] \times [N ] \to \{0, 1\}$ with reconstruction computed by degree-d polynomials with message size $N^{O(\log \log d/ \log d)}$. Combining our results with a lower bound of Beimel et al. [CRYPTO 2021], we show that increasing the degree of the reconstruction function in CDS protocols provably reduces the message size. To construct our schemes, we define sparse matching vectors, show constructions of such vectors, and design CDS protocols and secret-sharing schemes with degree-$d$ reconstruction from sparse matching vectors.
Last updated:  2023-09-26
Towards Practical Sleepy BFT
Dahlia Malkhi, Atsuki Momose, and Ling Ren
Bitcoin's longest-chain protocol pioneered consensus under dynamic participation, also known as sleepy consensus, where nodes do not need to be permanently active. However, existing solutions for sleepy consensus still face two major issues, which we address in this work. First, existing sleepy consensus protocols have high latency (either asymptotically or concretely). We tackle this problem and achieve $4\Delta$ latency ($\Delta$ is the bound on network delay) in the best case, which is comparable to classic BFT protocols without dynamic participation support. Second, existing protocols have to assume that the set of corrupt participants remains fixed throughout the lifetime of the protocol due to a problem we call \emph{costless simulation}. We resolve this problem and support growing participation of corrupt nodes. Our new protocol also offers several other important advantages, including support for arbitrary fluctuation of honest participation as well as an efficient recovery mechanism for new active nodes.
Last updated:  2023-09-26
Network-Agnostic Security Comes (Almost) for Free in DKG and MPC
Renas Bacho, Daniel Collins, Chen-Da Liu-Zhang, and Julian Loss
Distributed key generation (DKG) protocols are an essential building block for threshold cryptosystems. Many DKG protocols tolerate up to $t_s<n/2$ corruptions assuming a well-behaved synchronous network, but become insecure as soon as the network delay becomes unstable. On the other hand, solutions in the asynchronous model operate under arbitrary network conditions, but only tolerate $t_a<n/3$ corruptions, even when the network is well-behaved. In this work, we ask whether one can design a protocol that achieves security guarantees in either scenario. We show a complete characterization of network-agnostic DKG protocols, showing that the tight bound is $t_a+2t_s <n$. As a second contribution, we provide an optimized version of the network-agnostic MPC protocol by Blum, Liu-Zhang and Loss [CRYPTO'20] which improves over the communication complexity of their protocol by a linear factor. Moreover, using our DKG protocol, we can instantiate our MPC protocol in the plain PKI model, i.e., without the need to assume an expensive trusted setup. Our protocols incur the same communication complexity as state-of-the-art DKG and MPC protocols with optimal resilience in their respective purely synchronous and asynchronous settings, thereby showing that network-agnostic security comes (almost) for free.
Last updated:  2023-09-26
COMBINE: COMpilation and Backend-INdependent vEctorization for Multi-Party Computation
Benjamin Levy, Muhammad Ishaq, Ben Sherman, Lindsey Kennard, Ana Milanova, and Vassilis Zikas
Recent years have witnessed significant advances in programming technology for multi-party computation (MPC), bringing MPC closer to practice and wider applicability. Typical MPC programming frameworks focus on either front-end language design (e.g., Wysteria, Viaduct, SPDZ), or back-end protocol implementation (e.g., ABY, MOTION, SPDZ). We propose a methodology for an MPC compilation toolchain, which by mimicking the compilation methodology of classical compilers enables middle-end (i.e., machine-independent) optimizations, yielding significant improvements. We advance an intermediate language, which we call MPC-IR that can be viewed as the analogue of (enriched) Static Single Assignment (SSA) form. MPC-IR enables backend-independent optimizations in a close analogy to machine-independent optimizations in classical compilers. To demonstrate our approach, we focus on a specific backend-independent optimization, SIMD-vectorization: We devise a novel classical-compiler-inspired automatic SIMD vectorization on MPC-IR. To demonstrate backend independence and quality of our optimization, we evaluate our approach with two mainstream backend frameworks that support multiple types of MPC protocols, namely MOTION and MP-SPDZ, and show significant improvements across the board.
Last updated:  2023-09-26
Agile Cryptography: A Universally Composable Approach
Christian Badertscher, Michele Ciampi, and Aggelos Kiayias
Being capable of updating cryptographic algorithms is an inevitable and essential practice in cryptographic engineering. This cryptographic agility, as it has been called, is a fundamental desideratum for long term cryptographic system security that still poses significant challenges from a modeling perspective. For instance, current formulations of agility fail to express the fundamental security that is expected to stem from timely implementation updates, namely the fact that the system retains some of its security properties provided that the update is performed prior to the deprecated implementation becoming exploited. In this work we put forth a novel framework for expressing updateability in the context of cryptographic primitives within the universal composition model. Our updatable ideal functionality framework provides a general template for expressing the security we expect from cryptographic agility capturing in a fine-grained manner all the properties that can be retained across implementation updates. We exemplify our framework over two basic cryptographic primitives, digital signatures and non-interactive zero-knowledge (NIZK), where we demonstrate how to achieve updateability with consistency and backwards-compatibility across updates in a composable manner. We also illustrate how our notion is a continuation of a much broader scope of the concept of agility introduced by Acar, Belenkiy, Bellare, and Cash in Eurocrypt 2010 in the context of symmetric cryptographic primitives.
Last updated:  2023-09-26
Regularizers to the Rescue: Fighting Overfitting in Deep Learning-based Side-channel Analysis
Azade Rezaeezade and Lejla Batina
Despite considerable achievements of deep learning-based side-channel analysis, overfitting represents a significant obstacle in finding optimized neural network models. This issue is not unique to the side-channel domain. Regularization techniques are popular solutions to overfitting and have long been used in various domains. At the same time, the works in the side-channel domain show sporadic utilization of regularization techniques. What is more, no systematic study investigates these techniques' effectiveness. In this paper, we aim to investigate the regularization effectiveness on a randomly selected model, by applying four powerful and easy-to-use regularization techniques to eight combinations of datasets, leakage models, and deep learning topologies. The investigated techniques are $L_1$, $L_2$, dropout, and early stopping. Our results show that while all these techniques can improve performance in many cases, $L_1$ and $L_2$ are the most effective. Finally, if training time matters, early stopping is the best technique.
Last updated:  2023-09-26
On the Concrete Security of TLS 1.3 PSK Mode
Hannah Davis, Denis Diemert, Felix Günther, and Tibor Jager
The pre-shared key (PSK) handshake modes of TLS 1.3 allow for the performant, low-latency resumption of previous connections and are widely used on the Web and by resource-constrained devices, e.g., in the Internet of Things. Taking advantage of these performance benefits with optimal and theoretically-sound parameters requires tight security proofs. We give the first tight security proofs for the TLS 1.3 PSK handshake modes. Our main technical contribution is to address a gap in prior tight security proofs of TLS 1.3 which modeled either the entire key schedule or components thereof as independent random oracles to enable tight proof techniques. These approaches ignore existing interdependencies in TLS 1.3's key schedule, arising from the fact that the same cryptographic hash function is used in several components of the key schedule and the handshake more generally. We overcome this gap by proposing a new abstraction for the key schedule and carefully arguing its soundness via the indifferentiability framework. Interestingly, we observe that for one specific configuration, PSK-only mode with hash function SHA-384, it seems difficult to argue indifferentiability due to a lack of domain separation between the various hash function usages. We view this as an interesting insight for the design of protocols, such as future TLS versions. For all other configurations however, our proofs significantly tighten the security of the TLS 1.3 PSK modes, confirming standardized parameters (for which prior bounds provided subpar or even void guarantees) and enabling a theoretically-sound deployment.
Last updated:  2023-09-26
Orca: FSS-based Secure Training with GPUs
Neha Jawalkar, Kanav Gupta, Arkaprava Basu, Nishanth Chandran, Divya Gupta, and Rahul Sharma
Secure Two-party Computation (2PC) allows two parties to compute any function on their private inputs without revealing their inputs to each other. In the offline/online model for 2PC, correlated randomness that is independent of all inputs to the computation, is generated in a preprocessing (offline) phase and this randomness is then utilized in the online phase once the inputs to the parties become available. Most 2PC works focus on optimizing the online time as this overhead lies on the critical path. A recent paradigm for obtaining efficient 2PC protocols with low online cost is based on the cryptographic technique of function secret sharing (FSS). We build an end-to-end system ORCA to accelerate the computation of FSS-based 2PC protocols with GPUs. Next, we observe that the main performance bottleneck in such accelerated protocols is in storage (due to the large amount of correlated randomness), and we design new FSS-based 2PC protocols for several key functionalities in ML which reduce storage by up to 5×. Compared to prior state-of-the-art on secure training accelerated with GPUs in the same computation model (PIRANHA, Usenix Security 2022), we show that ORCA has 4% higher accuracy, 98× lesser communication, and is 26× faster on CIFAR-10. Moreover, maintaining training accuracy while using fixed-point needs stochastic truncations, and all prior works on secure fixed-point training (including PIRANHA) use insecure protocols for it. We provide the first secure protocol for stochastic truncations and build on it to provide the first evaluation of training with end-to-end security. For secure ImageNet inference, ORCA achieves sub-second latency for VGG-16 and ResNet-50, and outperforms the state-of-the-art by 8 − 103×.
Last updated:  2023-09-26
Unified View for Notions of Bit Security
Shun Watanabe and Kenji Yasunaga
A theoretical framework of the bit security of cryptographic primitives/games was first introduced in a pioneering work by Micciancio and Walter (Eurocrypt 2018), and an alternative framework was introduced by the authors (Asiacrypt 2021). First, we observe that quantitative results in the latter framework are preserved even if adversaries are allowed to output the failure symbol. With this slight modification, we show that the notion of bit security in the latter framework is equivalent to that in the former framework up to constant bits. Also, we demonstrate that several existing notions of advantages can be captured in a unified way. Based on this equivalence, we show that the reduction algorithm of Hast (J. Cryptology, 2004) gives a tight reduction of the Goldreich-Levin hard-core predicate to the hardness of one-way functions. These two results resolved open problems that remained. Furthermore, in the latter framework, we show that all games we need to care about are decision games. Namely, for every search game G, there is the corresponding decision game G′ such that G has λ-bit security if and only if G′ has λ-bit security. The game G′ consists of the real and the ideal games, where attacks in the ideal game are never approved. Such games often appear in game-hopping security proofs. The result justifies such security proofs because they lose no security. Finally, we provide a distribution replacement theorem. Suppose a game using distribution Q in a black-box manner is λ-bit secure, and two distributions P and Q are computationally λ-bit secure indistinguishable. In that case, the game where Q is replaced by P is also λ-bit secure.
Last updated:  2023-09-25
An Anonymous Multireceiver Hybrid Signcryption for Broadcast Communication
Alia Umrani, Apurva K Vangujar, and Paolo Palmieri
Confidentiality, authentication, and anonymity are the basic security requirements in broadcast communication, that can be achieved by Digital Signature (DS), encryption, and pseudo-identity (PID) techniques. Signcryption offers both DS and encryption more efficiently than "sign-then-encrypt,". However, compared to hybrid signcryption, it has higher computational and communication costs. Our paper proposes an Anonymous Multi-receiver Certificateless Hybrid Signcryption (AMCLHS) for secure broadcast communication. AMCLHS combines public-key cryptography and symmetric key to achieve confidentiality, authentication, and anonymity. We provide a simple and efficient construction of a multi-recipient Key Encapsulation Mechanism (mKEM) to create a symmetric session key. This symmetric session key, along with the sender's private key, is used in Data Encapsulation Mechanism (DEM) to signcrypt the message, thus providing confidentiality and authentication. It also generates identical ciphertext for multiple recipients while keeping their identities private by assigning a PID to each user. Our scheme demonstrate notions for Indistinguishability under Chosen-Ciphertext Attack using Elliptic Curve Computational Diffie-Hellman assumption in random oracle. It also demonstrates security for Existential Unforgeability against Chosen Message Attack using Elliptic Curve Diffie-Hellman assumption. The AMCLHS scheme operates in a multireceiver certificateless environment, preventing the key escrow problem. We show that, compared to existing schemes, our scheme is computationally efficient, provides optimal communication cost, and simultaneously ensures security properties such as confidentiality, authentication, anonymity, non-repudiation, and forward security.
Last updated:  2023-09-25
A Multireceiver Certificateless Signcryption (MCLS) Scheme
Alia Umrani, Apurva K Vangujar, and Paolo Palmieri
User authentication and message confidentiality are the basic security requirements of high-end applications such as multicast communication and distributed systems. Several efficient signature-then-encrypt cryptographic schemes have been proposed to offer these security requirements with lower computational cost and communication overhead. However, signature-then-encryption techniques take more computation time than signcryption techniques. Signcryption accomplishes both digital signature and public key encryption functions in a single logical step and at a much lower cost than ``signature followed by encryption.'' Several signcryption schemes based on bilinear pairing operations have been proposed. Similarly, anonymous multi-receiver encryption has recently risen in prominence in multicast communication and distributed settings, where the same messages are sent to several receivers but the identity of each receiver should remain private. Anonymous multi-receiver encryption allows a receiver to obtain the plaintext by decrypting the ciphertext using their own private key, while their identity is kept secret to anyone, including other receivers. Among the Certificateless Multi-receiver Encryption (CLMRE) schemes that have been introduced, Hung et al. proposed an efficient Anonymous Multireceiver Certificateless Encryption (AMCLE) scheme ensuring confidentiality and anonymity based on bilinear pairings and is secure against IND-CCA and ANON-CCA. In this paper, we substantially extend Hung et al.’s multireceiver certificateless encryption scheme to a Multireceiver Certificateless Signcryption (MCLS) scheme that provides confidentiality along with authentication. We show that, as compared to Hung et al.’s encryption scheme, our signcryption scheme requires only three additional multiplication operations for signcryption and unsigncryption phases. Whereas, the signcryption cost is linear with the number of designated receivers while the unsigncryption cost remains constant for each designated receiver. We compare the results with other existing single receiver and multireceiver signcryption schemes in terms of number of operations, exemption of key escrow problem, and public key settings. The scheme proposed in this paper is more efficient for single and multireceiver signcryption schemes while providing exemption from the key escrow problem, and working in certificateless public key settings.
Last updated:  2023-09-25
High-precision RNS-CKKS on fixed but smaller word-size architectures: theory and application
Rashmi Agrawal, Jung Ho Ahn, Flavio Bergamaschi, Ro Cammarota, Jung Hee Cheon, Fillipe D. M. de Souza, Huijing Gong, Minsik Kang, Duhyeong Kim, Jongmin Kim, Hubert de Lassus, Jai Hyun Park, Michael Steiner, and Wen Wang
A prevalent issue in the residue number system (RNS) variant of the Cheon-Kim-Kim-Song (CKKS) homomorphic encryption (HE) scheme is the challenge of efficiently achieving high precision on hardware architectures with a fixed, yet smaller, word-size of bit-length $W$, especially when the scaling factor satisfies $\log\Delta > W$. In this work, we introduce an efficient solution termed composite scaling. In this approach, we group multiple RNS primes as $q_\ell:= \prod_{j=0}^{t-1} q_{\ell,j}$ such that $\log q_{\ell,j} < W$ for $0\le j < t$, and use each composite $q_\ell$ in the rescaling procedure as $\mathsf{ct}\mapsto \lfloor \mathsf{ct} / q_\ell\rceil$. Here, the number of primes, denoted by $t$, is termed the composition degree. This strategy contrasts the traditional rescaling method in RNS-CKKS, where each $q_\ell$ is chosen as a single $\log\Delta$-bit prime, a method we designate as single scaling. To achieve higher precision in single scaling, where $\log\Delta > W$, one would either need a novel hardware architecture with word size $W' > \log\Delta$ or would have to resort to relatively inefficient solutions rooted in multi-precision arithmetic. This problem, however, doesn't arise in composite scaling. In the composite scaling approach, the larger the composition degree $t$, the greater the precision attainable with RNS-CKKS across an extensive range of secure parameters tailored for workload deployment. We have integrated composite scaling RNS-CKKS into both OpenFHE and Lattigo libraries. This integration was achieved via a concrete implementation of the method and its application to the most up-to-date workloads, specifically, logistic regression training and convolutional neural network inference. Our experiments demonstrate that single and composite scaling approaches are functionally equivalent, both theoretically and practically.
Last updated:  2023-09-25
Epochal Signatures for Deniable Group Chats
Andreas Hülsing and Fiona Johanna Weber
We introduce formal definitions for deniability in group chats by extending a pre-existing model that did not have this property. We then introduce “epochal signatures” as an almost drop-in replacement for signatures, which can be used to make certain undeniable group-chats deniable by just performing that replacement. Following that we provide a practical epochal signature scheme and prove its security.
Last updated:  2023-09-25
Onion Routing with Replies
Christiane Kuhn, Dennis Hofheinz, Andy Rupp, and Thorsten Strufe
Onion routing (OR) protocols are a crucial tool for providing anonymous internet communication. An OR protocol enables a user to anonymously send requests to a server. A fundamental problem of OR protocols is how to deal with replies: ideally, we would want the server to be able to send a reply back to the anonymous user without knowing or disclosing the user's identity. Existing OR protocols do allow for such replies, but do not provably protect the payload (i.e., message) of replies against manipulation. Kuhn et al. (IEEE S&P 2020) show that such manipulations can in fact be leveraged to break anonymity of the whole protocol. In this work, we close this gap and provide the first framework and protocols for OR with protected replies. We define security in the sense of an ideal functionality in the universal composability model, and provide corresponding (less complex) game-based security notions for the individual properties. We also provide two secure instantiations of our framework: one based on updatable encryption, and one based on succinct non-interactive arguments (SNARGs) to authenticate payloads both in requests and replies. In both cases, our central technical handle is an implicit authentication of the transmitted payload data, as opposed to an explicit, but insufficient authentication (with MACs) in previous solutions. Our results exhibit a new and surprising application of updatable encryption outside of long-term data storage.
Last updated:  2023-09-25
Post-quantum WireGuard
Andreas Hülsing, Kai-Chun Ning, Peter Schwabe, Fiona Johanna Weber, and Philip R. Zimmermann
In this paper we present PQ-WireGuard, a post-quantum variant of the handshake in the WireGuard VPN protocol (NDSS 2017). Unlike most previous work on post-quantum security for real-world protocols, this variant does not only consider post-quantum confidentiality (or forward secrecy) but also post-quantum authentication. To achieve this, we replace the Diffie-Hellman-based handshake by a more generic approach only using key-encapsulation mechanisms (KEMs). We establish security of PQ-WireGuard, adapting the security proofs for WireGuard in the symbolic model and in the standard model to our construction. We then instantiate this generic construction with concrete post-quantum secure KEMs, which we carefully select to achieve high security and speed. We demonstrate competitiveness of PQ-WireGuard presenting extensive benchmarking results comparing to widely deployed VPN solutions.
Last updated:  2023-09-25
Reversing, Breaking, and Fixing the French Legislative Election E-Voting Protocol
Alexandre Debant and Lucca Hirschi
We conduct a security analysis of the e-voting protocol used for the largest political election using e-voting in the world, the 2022 French legislative election for the citizens overseas. Due to a lack of system and threat model specifications, we built and contributed such specifications by studying the French legal framework and by reverse-engineering the code base accessible to the voters. Our analysis reveals that this protocol is affected by two design-level and implementation-level vulnerabilities. We show how those allow a standard voting server attacker and even more so a channel attacker to defeat the election integrity and ballot privacy due to 6 attack variants. We propose and discuss 5 fixes to prevent those attacks. Our specifications, the attacks, and the fixes were acknowledged by the relevant stakeholders during our responsible disclosure. Our attacks are in the process of being prevented with our fixes for future elections. Beyond this specific protocol, we draw general conclusions and lessons from this instructive experience where an e-voting protocol meets the real-world constraints of a large-scale and political election.
Last updated:  2023-09-25
Post Quantum Noise
Yawning Angel, Benjamin Dowling, Andreas Hülsing, Peter Schwabe, and Fiona Johanna Weber
We introduce PQNoise, a post-quantum variant of the Noise framework. We demonstrate that it is possible to replace the Diffie-Hellman key-exchanges in Noise with KEMs in a secure way. A challenge is the inability to combine key pairs of KEMs, which can be resolved by certain forms of randomness-hardening for which we introduce a formal abstraction. We provide a generic recipe to turn classical Noise patterns into PQNoise patterns. We prove that the resulting PQNoise patterns achieve confidentiality and authenticity in the fACCE-model. Moreover we show that for those classical Noise-patterns that have been conjectured or proven secure in the fACCE-model our matching PQNoise-patterns eventually achieve the same security. Our security proof is generic and applies to any valid PQNoise pattern. This is made possible by another abstraction, called a hash-object, which hides the exact workings of how keying material is processed in an abstract stateful object that outputs pseudorandom keys under different corruption patterns. We also show that the hash chains used in Noise are a secure hash-object. Finally, we demonstrate the practicality of PQNoise delivering benchmarks for several base patterns.
Last updated:  2023-09-25
Fuzzy Password-Authenticated Key Exchange
Pierre-Alain Dupont, Julia Hesse, David Pointcheval, Leonid Reyzin, and Sophia Yakoubov
Show abstract
Consider key agreement by two parties who start out knowing a common secret (which we refer to as “pass-string”, a generalization of “password”), but face two complications: (1) the pass-string may come from a low-entropy distribution, and (2) the two parties’ copies of the pass-string may have some noise, and thus not match exactly. We provide the first efficient and general solutions to this problem that enable, for example, key agreement based on commonly used biometrics such as iris scans. The problem of key agreement with each of these complications individually has been well studied in literature. Key agreement from low-entropy shared pass-strings is achieved by password-authenticated key exchange (PAKE), and key agreement from noisy but high-entropy shared pass-strings is achieved by information-reconciliation protocols as long as the two secrets are “close enough.” However, the problem of key agreement from noisy low-entropy pass-strings has never been studied. We introduce (universally composable) fuzzy password-authenticated key exchange (fPAKE), which solves exactly this problem. fPAKE does not have any entropy requirements for the pass-strings, and enables secure key agreement as long as the two pass-strings are “close” for some notion of closeness. We also give two constructions. The first construction achieves our fPAKE definition for any (efficiently computable) notion of closeness, including those that could not be handled before even in the high-entropy setting. It uses Yao’s garbled circuits in a way that is only two times more costly than their use against semi-honest adversaries, but that guarantees security against malicious adversaries. The second construction is more efficient, but achieves our fPAKE definition only for pass-strings with low Hamming distance. It builds on very simple primitives: robust secret sharing and PAKE.
Last updated:  2023-09-25
Compact Frequency Estimators in Adversarial Environments
Sam A. Markelon, Mia Filić, and Thomas Shrimpton
Count-Min Sketch (CMS) and HeavyKeeper (HK) are two realizations of a compact frequency estimator (CFE). These are a class of probabilistic data structures that maintain a compact summary of (typically) high-volume streaming data, and provides approximately correct estimates of the number of times any particular element has appeared. CFEs are often the base structure in systems looking for the highest-frequency elements (i.e., top-$K$ elements, heavy hitters, elephant flows). Traditionally, probabilistic guarantees on the accuracy of frequency estimates are proved under the implicit assumption that stream elements do not depend upon the internal randomness of the structure. Said another way, they are proved in the presence of data streams that are created by non-adaptive adversaries. Yet in many practical use-cases, this assumption is not well-matched with reality; especially, in applications where malicious actors are incentivized to manipulate the data stream. We show that the CMS and HK structures can be forced to make significant estimation errors, by concrete attacks that exploit adaptivity. We analyze these attacks analytically and experimentally, with tight agreement between the two. Sadly, these negative results seem unavoidable for (at least) sketch-based CFEs with parameters that are reasonable in practice. On the positive side, we give a new CFE (Count-Keeper) that can be seen as a composition of the CMS and HK structures. Count-Keeper estimates are typically more accurate (by at least a factor of two) than CMS for ``honest" streams; our attacks against CMS and HK are less effective (and more resource intensive) when used against Count-Keeper; and Count-Keeper has a native ability to flag estimates that are suspicious, which neither CMS or HK (or any other CFE, to our knowledge) admits.
Last updated:  2023-09-25
Sigmabus: Binding Sigmas in Circuits for Fast Curve Operations
George Kadianakis, Mary Maller, and Andrija Novakovic
This paper introduces Sigmabus, a technique designed to enhance the efficiency of zero-knowledge circuits by relocating computationally expensive operations outside the circuit. Specifically, Sigmabus focuses on moving elliptic curve group operations, typically proven with expensive non-native field arithmetic, to external computations. By leveraging Sigma protocols, elliptic curve group operations are proven outside the circuit, while additional constraints are applied to the circuit to ensure correct execution of the Sigma protocol. This approach can achieve significant performance improvements in zero-knowledge circuits. This paper presents the Sigmabus protocol along with its security proofs, and demonstrates its practical implications through various use cases.
Last updated:  2023-09-25
LegRoast: Efficient post-quantum signatures from the Legendre PRF
Ward Beullens and Cyprien Delpech de Saint Guilhem
We introduce an efficient post-quantum signature scheme that relies on the one-wayness of the Legendre PRF. This "LEGendRe One-wAyness SignaTure" (LegRoast) builds upon the MPC-in-the-head technique to construct an efficient zero-knowledge proof, which is then turned into a signature scheme with the Fiat-Shamir transform. Unlike many other Fiat-Shamir signatures, the security of LegRoast can be proven without using the forking lemma, and this leads to a tight (classical) ROM proof. We also introduce a generalization that relies on the one-wayness of higher-power residue characters; the "POwer Residue ChaRacter One-wAyness SignaTure" (PorcRoast). LegRoast outperforms existing MPC-in-the-head-based signatures (most notably Picnic/Picnic2) in terms of signature size and speed. Moreover, PorcRoast outperforms LegRoast by a factor of 2 in both signature size and signing time. For example, one of our parameter sets targeting NIST security level I results in a signature size of 7.2 KB and a signing time of 2.8ms. This makes PorcRoast the most efficient signature scheme based on symmetric primitives in terms of signature size and signing time.
Last updated:  2023-09-25
Fully Homomorphic Encryption-Based Protocols for Enhanced Private Set Intersection Functionalities
JINGWEI HU, Junyan Chen, Wangchen Dai, and Huaxiong Wang
This study delves into secure computations for set intersections using fully homomorphic encryption (FHE) within the semi-honest setting. Our protocols facilitate joint computations between two parties, each holding a set of inputs denoted as $N_s$ and $N_r$ in size, respectively. The primary objective is to determine various functionalities, such as intersection size and sum, while maintaining data confidentiality. These functionalities extend the classic private set intersection (PSI) and have practical applications in contact tracing, ad conversion analysis, and online dating, each abstracted into specialized PSI protocols. Our work demonstrates that these extended PSI functionalities are interconnected, with the PSI-cardinality protocol serving as the foundation. By adapting this protocol, we naturally arrive at PSI-sum-cardinality. Additionally, PSI-token-threshold is achieved by augmenting PSI-cardinality with FHE-based oblivious polynomial evaluation (OPE). The tPSI protocol combines PSI-token-threshold and standard PSI, allowing information sharing when the intersection size exceeds a threshold. Our protocols excel in simplicity, enhancing ease of understanding, implementation, optimization, and long-term maintenance. They also exhibit sublinear communication complexity concerning the larger sender's set, rendering them well-suited for scenarios involving substantial data. Various optimization techniques further bolster their practical efficiency.
Last updated:  2023-09-25
Quantum Lattice Enumeration in Limited Depth
Nina Bindel, Xavier Bonnetain, Marcel Tiepelt, and Fernando Virdia
In 2018, Aono et al. (ASIACRYPT 2018) proposed to use quantum backtracking algorithms (Montanaro, TOC 2018; Ambainis and Kokainis, STOC 2017) to speedup lattice point enumeration. Quantum lattice sieving algorithms had already been proposed (Laarhoven et al., PQCRYPTO 2013), being shown to provide an asymptotic speedup over classical counterparts, but also to lose competitivity at relevant dimensions to cryptography if practical considerations on quantum computer architecture were taken into account (Albrecht et al., ASIACRYPT 2020). Aono et al.’s work argued that quantum walk speedups can be applied to lattice enumeration, achieving at least a quadratic asymptotic speedup à la Grover search while not requiring exponential amounts of quantum accessible classical memory, as it is the case for sieving. In this work, we explore how to lower bound the cost of using Aono et al.’s techniques on lattice enumeration with extreme cylinder pruning assuming a limit to the maximum depth that a quantum computation can achieve without decohering, with the objective of better understanding the practical applicability of quantum backtracking in lattice cryptanalysis.
Last updated:  2023-09-25
Lattice-Based Polynomial Commitments: Towards Asymptotic and Concrete Efficiency
Giacomo Fenzi and Ngoc Khanh Nguyen
Polynomial commitments schemes are a powerful tool that enables one party to commit to a polynomial $p$ of degree $d$, and prove that the committed function evaluates to a certain value $z$ at a specified point $u$, i.e. $p(u) = z$, without revealing any additional information about the polynomial. Recently, polynomial commitments have been extensively used as a cryptographic building block to transform polynomial interactive oracle proofs (PIOPs) into efficient succinct arguments. In this paper, we propose a lattice-based polynomial commitment that achieves succinct proof size and verification time in the degree $d$ of the polynomial. Extractability of our scheme holds in the random oracle model under a natural ring version of the BASIS assumption introduced by Wee and Wu (EUROCRYPT 2023). Unlike recent constructions of polynomial commitments by Albrecht et al. (CRYPTO 2022), and by Wee and Wu, we do not require any expensive preprocessing steps, which makes our scheme particularly attractive as an ingredient of a PIOP compiler for succinct arguments. We further instantiate our polynomial commitment, together with the Marlin PIOP (Eurocrypt 2020), to obtain a publicly-verifiable trusted-setup succinct argument for Rank-1 Constraint System (R1CS). Performance-wise, we achieve 26 MB proof size for $2^{20}$ constraints, which is 10X smaller than currently the only publicly-verifiable lattice-based SNARK proposed by Albrecht et al.
Last updated:  2023-09-25
On vectorial functions mapping strict affine subspaces of their domain into strict affine subspaces of their co-domain, and the strong D-property
Claude Carlet and Enrico Piccione
Given three positive integers $n<N$ and $M$, we study those functions $\mathcal{F}$ from the vector space $\mathbb{F}_2^N$ (possibly endowed with the field structure) to $\mathbb{F}_2^M$, which map at least one $n$-dimensional affine subspace of $\mathbb{F}_2^N$ into an affine subspace whose dimension is less than $M$, possibly equal to $n$. This provides functions from $\mathbb{F}_2^n$ to $\mathbb{F}_2^m$ for some $m$ (and in some cases, permutations) that have a simple representation over $\mathbb{F}_2^N$ or over $\mathbb{F}_{2^N}$. We show that the nonlinearity of $\mathcal{F}$ must not be too large for allowing this and we observe that if it is zero, there automatically exists a strict affine subspace of its domain that is mapped by $\mathcal{F}$ into a strict affine subspace of its co-domain. In this case, we show that the nonlinearity of the restriction may be large. We study the other cryptographic properties of such restriction, viewed as an $(n,m)$-function (resp. an $(n,n)$-permutation). We then focus on the case of an $(N,N)$-function $\mathcal{F}$ of the form $\psi(\mathcal{G}(x))$ where $\mathcal{G}$ is almost perfect nonlinear (APN) and $\psi$ is a linear function with a kernel of dimension $1.$ We observe that the restriction of $\mathcal{G}$ to an affine hyperplane $A$ has the D-property (introduced by Taniguchi after a result from Dillon) as an $(N-1,N)$-function, if and only if, for every such $\psi$, the restriction of $\mathcal{F}(x)=\psi(\mathcal{G}(x))$ to $A$ is not an APN $(N-1,N-1)$-function. If this holds for all affine hyperplanes $A,$ we say that $\mathcal{G}$ has the strong D-property. We note that not satisfying this cryptographically interesting property also has a positive aspect, since it allows to construct APN $(N-1,N-1)$-functions from $\mathcal{G}$. We give a characterization of the strong D-property for crooked functions (a particular case of APN functions) by means of their ortho-derivatives and we prove that the Gold APN function in dimension $N\geq 9$ odd does have the strong D-property (we also give a simpler proof that the strong D-property of the Gold APN function in even dimension $N\geq 6$ holds if and only if $N=6$ or $N\geq 8$). Then we give a partial result on the Dobbertin APN power function, and on this basis, we conjecture that it has the strong D-property as well. We then move our focus to two known infinite families of differentially 4-uniform $(N-1,N-1)$-permuta\-tions constructed as the restrictions of $(N,N)$-functions $\mathcal{F}(x)=\psi(\mathcal{G}(x))$ or $\mathcal{F}(x)=\psi(\mathcal{G}(x))+x$ where $\psi$ and $\mathcal{G}$ are as before, with the extra hypothesis that $\mathcal{G}$ is an APN permutation. After a deeper investigation on these classes, we provide proofs (which were missing) that they are not APN in dimension $n=N-1$ even.
Last updated:  2023-09-24
The wrong use of FESTA trapdoor functions leads to an adaptive attack
Tomoki Moriya
Isogeny-based cryptography is one of the candidates for post-quantum cryptography. In 2023, Kani's theorem breaks some isogeny-based schemes including SIDH, which was considered as a promising post-quantum scheme. Though Kani's theorem damaged isogeny-based cryptography, some researchers try to dig into the applications of Kani's theorem. A FESTA trapdoor function is an isogeny-based trapdoor function that is one trial to apply Kani's theorem to cryptography. The claim of this paper is that there is an adaptive attack if the FESTA trapdoor function is used without checking whether the matrix in the input is correct. In this paper, we provide an adaptive attack for FESTA trapdoor functions using a specific oracle. Our attack reveals the secret key of the function. This oracle may be constructed if FESTA trapdoor functions are used in the wrong way (\textit{i.e.,} without the checking process of the matrix). As an example, we explain that our attack can be adapted to a possible PKE scheme based on FESTA trapdoor functions in the wrong way. Our attack cannot be adapted to IND-CCA PKE schemes named FESTA proposed in the FESTA original paper.
Last updated:  2023-09-24
Tri-State Circuits: A Circuit Model that Captures RAM
David Heath, Vladimir Kolesnikov, and Rafail Ostrovsky
We introduce tri-state circuits (TSCs). TSCs form a natural model of computation that, to our knowledge, has not been considered by theorists. The model captures a surprising combination of simplicity and power. TSCs are simple in that they allow only three wire values ($0,1,$ and undefined - $\mathcal{Z}$) and three types of fan-in two gates; they are powerful in that their statically placed gates fire (execute) eagerly as their inputs become defined, implying orders of execution that depend on input. This behavior is sufficient to efficiently evaluate RAM programs. We construct a TSC that emulates $T$ steps of any RAM program and that has only $O(T \cdot \log^3 T \cdot \log \log T)$ gates. Contrast this with the reduction from RAM to Boolean circuits, where the best approach scans all of memory on each access, incurring quadratic cost. We connect TSCs with cryptography by using them to improve Yao's Garbled Circuit (GC) technique. TSCs capture the power of garbling far better than Boolean Circuits, offering a more expressive model of computation that leaves per-gate cost essentially unchanged. As an important application, we construct authenticated Garbled RAM (GRAM), enabling constant-round maliciously-secure 2PC of RAM programs. Let $\lambda$ denote the security parameter. We extend authenticated garbling to TSCs; by simply plugging in our TSC-based RAM, we obtain authenticated GRAM running at cost $O(T \cdot \log^3 T \cdot \log \log T \cdot \lambda)$, outperforming all prior work, including prior semi-honest GRAM. We also give semi-honest garbling of TSCs from a one-way function (OWF). This yields OWF-based GRAM at cost $O(T \cdot \log^3 T \cdot \log \log T \cdot \lambda)$, outperforming the best prior OWF-based GRAM by more than factor $\lambda$.
Last updated:  2023-09-24
KpqBench: Performance and Implementation Security Analysis of KpqC Competition Round 1 Candidates
YongRyeol Choi, MinGi Kim, YoungBeom Kim, JinGyo Song, JaeHwan Jin, HeeSeok Kim, and Seog Chung Seo
As the global migration to post-quantum cryptography (PQC) continues to progress actively, in Korea, the Post-Quantum Cryptography Research Center has been established to acquire PQC technology, leading the KpqC Competition. In February 2022, the KpqC Competition issued a call for proposals for PQC algorithms. By November 2022, a total of 16 candidates were selected for the first round (7 KEMs and 9 DSAs). Currently, round 1 submissions are being evaluated with respect to security, efficiency, and scalability in various environments. At the current stage, evaluating the software through an analysis to improve the software quality of the first-round submissions is judged appropriately. In this paper, we present analysis results regarding performance and implementation security on based dependency-free approach of external libraries. Namely, we configure extensive tests for an analysis with no dependencies by replacing external libraries that can complicate the build process with hard coding. From the performance perspective, we provide analysis results of performance profiling, execution time, and memory usage for each of KpqC candidates. From the implementation security perspective, we examine bugs and errors in the actual implementations using Valgrind software, metamorphic testing methodology that can include wide test coverage and constant-time implementation against the timing attack. As a result, we found implementation bugs and errors in two submissions, metamorphic testing errors in one submission, and non-constant-time implementation in one submission. Until the KpqC standard algorithm is announced, we argue that continuous integration of extensive tests will lead to higher-level software quality of KpqC candidates.
Last updated:  2023-09-24
Improving the Rectangle Attack on GIFT-64
Yincen Chen, Nana Zhang, Xuanyu Liang, Ling Song, Qianqian Yang, and Zhuohui Feng
GIFT is a family of lightweight block ciphers based on SPN structure and composed of two versions named GIFT-64 and GIFT-128. In this paper, we reevaluate the security of GIFT-64 against the rectangle attack under the related-key setting. Investigating the previous rectangle key recovery attack on GIFT-64, we obtain the core idea of improving the attack——trading off the time complexity of each attack phase. We flexibly guess part of the involved subkey bits to balance the time cost of each phase so that the overall time complexity of the attack is reduced. Moreover, the reused subkey bits are identified according to the linear key schedule of GIFT-64 and bring additional advantages for our attacks. Furthermore, we incorporate the above ideas and propose a dedicated MILP model for finding the best rectangle key recovery attack on GIFT-64. As a result, we get the improved rectangle attacks on 26-round GIFT-64, which are the best attacks on it in terms of time complexity so far.
Last updated:  2023-09-24
Cascade: Leaderless State-Machine Replication with High Throughput
Hao Lu, Jian Liu, and Kui Ren
State-machine replication (SMR) allows a state machine to be replicated across a set of replicas and handle clients' requests as a single machine. Most existing SMR protocols are leader-based, i.e., requiring a leader to order requests and coordinate the protocol. This design places a disproportionately high load on the leader, inevitably impairing the scalability. If the leader fails, a complex and bug-prone fail-over protocol is needed to switch to a new leader. An adversary can also exploit the fail-over protocol to slow down the protocol. In this paper, we propose a crash-fault tolerant SMR named Cascade, with the following properties: • Leaderless: it does not require a leader, hence completely get rid of the fail-over protocol. • Scalable: it can scale to a large number of replicas. %its throughput increases with the number of replicas. • Robust: it behaves well even under a poor network connection. We provide a full-fledged implementation of Cascade and systematically evaluate its performance. Our benchmark results show that Cascade achieves a peak throughput of around two million TPS, up to 8.7$\times$ higher than the state-of-the-art leaderless SMR.
Last updated:  2023-09-24
Do Private Transaction Pools Mitigate Frontrunning Risk?
Agostino Capponi, Ruizhe Jia, and Ye Wang
Blockchain users who submit transactions through private pools are guaranteed pre-trade privacy but face execution risk. We argue that private pools serve the intended purpose of eliminating frontrunning risk, only if such risk is high. Otherwise, some validators may decide to avoid monitoring private pools to preserve rents extracted from frontrunning bots. Private pools intensify the execution arms race for bots, thus decreasing their payoffs {and increasing validators' rents}. The private pool option reduces blockspace allocative inefficiencies and raises aggregate welfare.
Last updated:  2023-09-23
Rigorous Foundations for Dual Attacks in Coding Theory
Charles Meyer-Hilfiger and Jean-Pierre Tillich
Dual attacks aiming at decoding generic linear codes have been found recently to outperform for certain parameters information set decoding techniques which have been for $60$ years the dominant tool for solving this problem and choosing the parameters of code-based cryptosystems. However, the analysis of the complexity of these dual attacks relies on some unproven assumptions that are not even fully backed up with experimental evidence. These dual attacks can actually be viewed as the code-based analogue of dual attacks in lattice based cryptography. Here too, dual attacks have been found out those past years to be strong competitors to primal attacks and a controversy has emerged whether similar heuristics made for instance on the independence of certain random variables really hold. We will show that the dual attacks in coding theory can be studied by providing in a first step a simple alternative expression of the fundamental quantity used in these dual attacks. We then show that this expression can be studied without relying on independence assumptions whatsoever. This study leads us to discover that there is indeed a problem with the latest and most powerful dual attack introduced in the recent Asiacrypt 2022 paper "Statistical decoding 2.0: Reducing Decoding to LPN" (RLPN) and that for the parameters chosen in this algorithm there are indeed false candidates which are produced and which are not predicted by the analysis provided there which relies on independence assumptions. We then suggest a slight modification of this algorithm consisting in a further verification step, analyze it thoroughly, provide experimental evidence that our analysis is accurate and show that the complexity claims made in RLPN are indeed valid for this modified algorithm. This approach provides a simple methodology for studying rigorously dual attacks which could turn out to be useful for further developing the subject.
Last updated:  2023-09-23
Batching Cipolla-Lehmer-Müller's square root algorithm with hashing to elliptic curves
Dmitrii Koshelev
The present article provides a novel hash function $\mathcal{H}$ to any elliptic curve of $j$-invariant $\neq 0, 1728$ over a finite field $\mathbb{F}_{\!q}$ of large characteristic. The unique bottleneck of $\mathcal{H}$ consists in extracting a square root in $\mathbb{F}_{\!q}$ as well as for most hash functions. However, $\mathcal{H}$ is designed in such a way that the root can be found by (Cipolla--Lehmer--)Müller's algorithm in constant time. Violation of this security condition is known to be the only obstacle to applying the given algorithm in the cryptographic context. When the field $\mathbb{F}_{\!q}$ is highly $2$-adic and $q \equiv 1 \ (\mathrm{mod} \ 3)$, the new batching technique is the state-of-the-art hashing solution except for some sporadic curves. Indeed, Müller's algorithm costs $\approx 2\log_2(q)$ multiplications in $\mathbb{F}_{\!q}$. In turn, original Tonelli--Shanks's square root algorithm and all of its subsequent modifications have the asymptotic complexity $\Theta(\log(q) + g(\nu))$, where $\nu$ is the $2$-adicity of $\mathbb{F}_{\!q}$ and a function $g(\nu) \neq O(\nu)$. As an example, it is shown that Müller’s algorithm actually needs several times fewer multiplications in the field $\mathbb{F}_{\!q}$ (whose $\nu = 96$) of the standardized curve NIST P-224.
Last updated:  2023-09-23
Identity-Based Threshold Signatures from Isogenies
Shahla Atapoor
The identity-based signature, initially introduced by Shamir [Sha84], plays a fundamental role in the domain of identity-based cryptography. It offers the capability to generate a signature on a message, allowing any user to verify the authenticity of the signature using the signer's identifier information (e.g., an email address), instead of relying on a public key stored in a digital certificate. Another significant concept in practical applications is the threshold signature, which serves as a valuable tool for distributing the signing authority. The notion of an identity-based threshold signature scheme pertains to the distribution of a secret key associated with a specific identity among multiple entities, rather than depending on a master secret key generated by a public key generator. This approach enables a qualified group of participants to jointly engage in the signing process. In this paper, we present two identity-based threshold signature schemes based on isogenies, each of which addresses a different aspect of security. The first scheme prioritizes efficiency but offers security with abort, while the second scheme focuses on robustness. Both schemes ensure active security in the quantum random oracle model. To build these identity-based threshold signatures, we begin by modifying the identity-based signature scheme proposed by Shaw and Dutta [SD21], to accommodate the CSI-SharK signature scheme. Subsequently, we leverage the resulting identity-based signature and build two threshold schemes within the CSIDH (Commutative Supersingular Isogeny Diffie-Hellman) framework. Our proposed identity-based threshold signatures are designed based on CSI-SharK and can be easily adapted with minimal adjustments to function with CSI-FiSh.
Last updated:  2023-09-23
Fast batched asynchronous distributed key generation
Jens Groth and Victor Shoup
We present new protocols for threshold Schnorr signatures that work in an asynchronous communication setting, providing robustness and optimal resilience. These protocols provide unprecedented performance in terms of communication and computational complexity. In terms of communication complexity, for each signature, a single party must transmit a few dozen group elements and scalars across the network (independent of the size of the signing committee). In terms of computational complexity, the amortized cost for one party to generate a signature is actually less than that of just running the standard Schnorr signing or verification algorithm (at least for moderately sized signing committees, say, up to 100). For example, we estimate that with a signing committee of 49 parties, at most 16 of which are corrupt, we can generate 50,000 Schnorr signatures per second (assuming each party can dedicate one standard CPU core and 500Mbs of network bandwidth to signing). Importantly, this estimate includes both the cost of an offline precomputation phase (which just churns out message independent "presignatures") and an online signature generation phase. Also, the online signing phase can generate a signature with very little network latency (just one to three rounds, depending on how throughput and latency are balanced). To achieve this result, we provide two new innovations. One is a new secret sharing protocol (again, asynchronous, robust, optimally resilient) that allows the dealer to securely distribute shares of a large batch of ephemeral secret keys, and to publish the corresponding ephemeral public keys. To achieve better performance, our protocol minimizes public-key operations, and in particular, is based on a novel technique that does not use the traditional technique based on "polynomial commitments". The second innovation is a new algorithm to efficiently combine ephemeral public keys contributed by different parties (some possibly corrupt) into a smaller number of secure ephemeral public keys. This new algorithm is based on a novel construction of a so-called "super-invertible matrix" along with a corresponding highly-efficient algorithm for multiplying this matrix by a vector of group elements. As protocols for verifiably sharing a secret key with an associated public key and the technology of super-invertible matrices both play a major role in threshold cryptography and multi-party computation, our two new innovations should have applicability well beyond that of threshold Schnorr signatures.
Last updated:  2023-09-23
Non-Interactive Anonymous Router with Quasi-Linear Router Computation
Rex Fernando, Elaine Shi, Pratik Soni, Nikhil Vanjani, and Brent Waters
Anonymous routing is an important cryptographic primitive that allows users to communicate privately on the Internet, without revealing their message contents or their contacts. Until the very recent work of Shi and Wu (Eurocrypt’21), all classical anonymous routing schemes are interactive protocols, and their security rely on a threshold number of the routers being honest. The recent work of Shi and Wu suggested a new abstraction called Non-Interactive Anonymous Router (NIAR), and showed how to achieve anonymous routing non-interactively for the first time. In particular, a single untrusted router receives a token which allows it to obliviously apply a permutation to a set of encrypted messages from the senders. Shi and Wu’s construction suffers from two drawbacks: 1) the router takes time quadratic in the number of senders to obliviously route their messages; and 2) the scheme is proven secure only in the presence of static corruptions. In this work, we show how to construct a non-interactive anonymous router scheme with sub-quadratic router computation, and achieving security in the presence of adaptive corruptions. To get this result, we assume the existence of indistinguishability obfuscation and one-way functions. Our final result is obtained through a sequence of stepping stones. First, we show how to achieve the desired efficiency, but with security under static corruption and in a selective, single-challenge setting. Then, we go through a sequence of upgrades which eventually get us the final result. We devise various new techniques along the way which lead to some additional results. In particular, our techniques for reasoning about a network of obfuscated programs may be of independent interest.
Last updated:  2023-09-23
A Further Study of Vectorial Dual-Bent Functions
Jiaxin Wang, Fang-Wei Fu, Yadi Wei, and Jing Yang
Vectorial dual-bent functions have recently attracted some researchers' interest as they play a significant role in constructing partial difference sets, association schemes, bent partitions and linear codes. In this paper, we further study vectorial dual-bent functions $F: V_{n}^{(p)}\rightarrow V_{m}^{(p)}$, where $2\leq m \leq \frac{n}{2}$, $V_{n}^{(p)}$ denotes an $n$-dimensional vector space over the prime field $\mathbb{F}_{p}$. We give new characterizations of certain vectorial dual-bent functions (called vectorial dual-bent functions with Condition A) in terms of amorphic association schemes, linear codes and generalized Hadamard matrices, respectively. When $p=2$, we characterize vectorial dual-bent functions with Condition A in terms of bent partitions. Furthermore, we characterize certain bent partitions in terms of amorphic association schemes, linear codes and generalized Hadamard matrices, respectively. For general vectorial dual-bent functions $F: V_{n}^{(p)}\rightarrow V_{m}^{(p)}$ with $F(0)=0, F(x)=F(-x)$ and $2\leq m \leq \frac{n}{2}$, we give a necessary and sufficient condition on constructing association schemes. Based on such a result, more association schemes are constructed from vectorial dual-bent functions.
Last updated:  2023-09-22
Provable Security Analysis of the Secure Remote Password Protocol
Dennis Dayanikli and Anja Lehmann
This paper analyses the Secure Remote Password Protocol (SRP) in the context of provable security. SRP is an asymmetric Password-Authenticated Key Exchange (aPAKE) protocol introduced in 1998. It allows a client to establish a shared cryptographic key with a server based on a password of potentially low entropy. Although the protocol was part of several standardization efforts, and is deployed in numerous commercial applications such as Apple Homekit, 1Password or Telegram, it still lacks a formal proof of security. This is mainly due to some of the protocol's design choices which were implemented to circumvent patent issues. Our paper gives the first security analysis of SRP in the universal composability (UC) framework. We show that SRP is UC-secure against passive eavesdropping attacks under the standard CDH assumption in the random oracle model. We then highlight a major protocol change designed to thwart active attacks and propose a new assumption -- the additive Simultaneous Diffie Hellman (aSDH) assumption -- under which we can guarantee security in the presence of an active attacker. Using this new assumption as well as the Gap CDH assumption, we prove security of the SRP protocol against active attacks. Our proof is in the "Angel-based UC framework", a relaxation of the UC framework which gives all parties access to an oracle with super-polynomial power. In our proof, we assume that all parties have access to a DDH oracle (limited to finite fields). We further discuss the plausibility of this assumption and which level of security can be shown without it.
Last updated:  2023-09-22
The Generating Series of Support Minors MinRank Ideals
Daniel Smith-Tone
The support minors method has become indispensable to cryptanalysts in attacking various post-quantum cryptosystems in the areas of multivariate cryptography and rank-based cryptography. The complexity analysis for support minors minrank calculations is a bit messy, with no closed form for the Hilbert series of the ideal generated by the support minors equations (or, more correctly, for the quotient of the polynomial ring by this ideal). In this article, we provide a generating series whose coefficients are the Hilbert Series of related MinRank ideals. This simple series therefore reflects and relates the structure of all support minors ideals. Its simplicity also makes it practically useful in computing the complexity of support minors instances.
Last updated:  2023-09-22
Efficient Secure Two Party ECDSA
Sermin Kocaman and Younes Talibi Alaoui
Distributing the Elliptic Curve Digital Signature Algorithm (ECDSA) has received increased attention in past years due to the wide range of applications that can benefit from this, particularly after the popularity that the blockchain technology has gained. Many schemes have been proposed in the literature to improve the efficiency of multi- party ECDSA. Most of these schemes either require heavy homomorphic encryption computation or multiple executions of a functionality that transforms Multiplicative shares to Additive shares (MtA). Xue et al. (CCS 2021) proposed a 2-party ECDSA protocol secure against mali- cious adversaries and only requires one execution of MtA, with an online phase that consists of only one party sending one field element to the other party with a computational overhead dominated by the verifica- tion step of the signature scheme. We propose a novel protocol, based on the assumption that the Computational Diffie-Hellman problem is hard, that offers the same online phase performance as the protocol of Xue et al., but improves the offline phase by reducing the computational cost by one elliptic curve multiplication and the communication cost by two field elements. To the best of our knowledge, our protocol offers the most efficient offline phase for a two-party ECDSA protocol with such an efficient online phase.
Last updated:  2023-09-22
Scalable Off-Chain Auctions
Mohsen Minaei, Duc V. Le, Ranjit Kumaresan, Andrew Beams, Pedro Moreno-Sanchez, Yibin Yang, Srinivasan Raghuraman, Panagiotis Chatzigiannis, and Mahdi Zamani
Blockchain auction plays an important role in the price discovery of digital assets (e.g. NFTs). However, despite their importance, implementing auctions directly on blockchains such as Ethereum incurs scalability issues. In particular, the on-chain transactions scale poorly with the number of bidders, leading to network congestion, increased transaction fees, and slower transaction confirmation time. This lack of scalability significantly hampers the ability of the system to handle large-scale, high-speed auctions that are common in today's economy. In this work, we build a protocol where an auctioneer can conduct sealed bid auctions that run entirely off-chain when parties behave honestly, and in the event that $k$ bidders deviate (e.g., do not open their sealed bid) from an $n$-party auction protocol, then the on-chain complexity is only $O(k \log n)$. This improves over existing solutions that require $O(n)$ on-chain complexity, even if a single bidder deviates from the protocol. In the event of a malicious auctioneer, our protocol still guarantees that the auction will successfully terminate. We implement our protocol and show that it offers significant efficiency improvements compared to existing on-chain solutions. Our use of zkSnark to achieve scalability also ensures that the on-chain contract and other participants do not acquire any information about the bidders' identities and their respective bids, except for the winner and the winning bid amount.
Last updated:  2023-09-22
Preimage and Collision Attacks on Reduced Ascon Using Algebraic Strategies
Qinggan Fu, Ye Luo, Qianqian Yang, and Ling Song
Ascon, a family of algorithms that supports hashing and authenticated encryption, is the winner of the NIST Lightweight Cryptography Project. In this paper, we propose an improved preimage attack against 2-round Ascon-XOF-64 with a complexity of $2^{32}$ via a better guessing strategy. Furthermore, in order to find a good guessing strategy efficiently, we build a MILP model and successfully extend the attack to 3 rounds. The time complexity is $2^{53}$ when $IV=0$, while for the real $IV$, the attack still works and the time complexity is $2^{51}$. Additionally, we also investigate the resistance of Ascon-HASH against collision attacks. We introduce the linearization of the inverse of S-boxes and then propose a practical free-start collision attack on 3-round Ascon-HASH using a differential trail searched dedicatedly. Furthermore, We construct different 2-round connectors using the linearization of the inverse of S-boxes and successfully extend the collision attack to 4 rounds and 5 rounds of Ascon-HASH with complexities of $2^{21}$ and $2^{41}$ respectively. Although our attacks do not compromise the security of the full 12-round Ascon-XOF and Ascon-HASH, they provide some insights into Ascon's security.
Last updated:  2023-09-22
Commitments with Efficient Zero-Knowledge Arguments from Subset Sum Problems
Jules Maire and Damien Vergnaud
We present a cryptographic string commitment scheme that is computationally hiding and binding based on (modular) subset sum problems. It is believed that these NP-complete problems provide post-quantum security contrary to the number theory assumptions currently used in cryptography. Using techniques recently introduced by Feneuil, Maire, Rivain and Vergnaud, this simple commitment scheme enables an efficient zero-knowledge proof of knowledge for committed values as well as proofs showing Boolean relations amongst the committed bits. In particular, one can prove that committed bits $m_0, m_1, ..., m_\ell$ satisfy $m_0 = C(m_1, ..., m_\ell)$ for any Boolean circuit $C$ (without revealing any information on those bits). The proof system achieves good communication and computational complexity since for a security parameter $\lambda$, the protocol's communication complexity is $\tilde{O}(|C| \lambda + \lambda^2)$ (compared to $\tilde{O}(|C| \lambda^2)$ for the best code-based protocol due to Jain, Krenn, Pietrzak and Tentes).
Last updated:  2023-09-22
Counting Unpredictable Bits: A Simple PRG from One-way Functions
Noam Mazor and Rafael Pass
A central result in the theory of Cryptography, by Hastad, Imagliazzo, Luby and Levin [SICOMP’99], demonstrates that the existence one-way functions (OWF) implies the existence of pseudo-random generators (PRGs). Despite the fundamental importance of this result, and several elegant improvements/simplifications, analyses of constructions of PRGs from OWFs remain complex (both conceptually and technically). Our goal is to provide a construction of a PRG from OWFs with a simple proof of security; we thus focus on the setting of non-uniform security (i.e., we start off with a OWF secure against non-uniform PPT, and we aim to get a PRG secure against non-uniform PPT). Our main result is a construction of a PRG from OWFs with a self-contained, simple, proof of security, relying only on the Goldreich-Levin Theorem (and the Chernoff bound). Although our main goal is simplicity, the construction, and a variant there-of, also improves the efficiency—in terms of invocations and seed lengths—of the state-of-the-art constructions due to [Haitner-Reingold-Vadhan, STOC’10] and [Vadhan-Zheng, STOC’12], by a factor $O(\log^2 n)$. The key novelty in our analysis is a generalization of the Blum-Micali [FOCS’82] notion of unpredictabilty—rather than requiring that every bit in the output of a function is unpredictable, we count how many unpredictable bits a function has, and we show that any OWF on $n$ input bits (after hashing the input and the output) has $n + O(\log n)$ unpredictable output bits. Such unpredictable bits can next be “extracted” into a pseudorandom string using standard techniques.
Last updated:  2023-09-22
Post-Quantum Fully Homomorphic Encryption with Group Ring Homomorphisms
Christopher Leonardi and Maya Gusak
Gentry's groundbreaking work showed that a fully homomorphic, provably secure scheme is possible via bootstrapping a somewhat homomorphic scheme. However, a major drawback of bootstrapping is its high computational cost. One alternative is to use a different metric for noise so that homomorphic operations do not accumulate noise, eliminating the need for boostrapping altogether. Leonardi and Ruiz-Lopez present a group-theoretic framework for such a ``noise non-accumulating'' multiplicative homomorphic scheme, but Agathocleous et al. expose weaknesses in this framework when working over finite abelian groups. Tangentially, Li and Wang present a ``noise non-accumulating'' fully homomorphic scheme by performing Ostrovsky and Skeith's transform on a multiplicative homomorphic scheme of non-abelian group rings. Unfortunately, the security of Li and Wang's scheme relies on the Factoring Large Numbers assumption, which is false given an adversary with a quantum computer. In this work, we seek to modify Li and Wang's scheme to be post-quantum secure by fitting it into the Leonardi and Ruiz-Lopez framework for non-abelian rings. We discuss improved security assumptions for Li and Wang encryption and assess the shortcomings of working in a non-abelian setting. Finally, we show that a large class of semisimple rings is incompatible with the Leonardi and Ruiz-Lopez framework.
Last updated:  2023-09-22
Two-Round Concurrent 2PC from Sub-Exponential LWE
Behzad Abdolmaleki, Saikrishna Badrinarayanan, Rex Fernando, Giulio Malavolta, Ahmadreza Rahimi, and Amit Sahai
Secure computation is a cornerstone of modern cryptography and a rich body of research is devoted to understanding its round complexity. In this work, we consider two-party computation (2PC) protocols (where both parties receive output) that remain secure in the realistic setting where many instances of the protocol are executed in parallel (concurrent security). We obtain a two-round concurrent-secure 2PC protocol based on a single, standard, post-quantum assumption: The subexponential hardness of the learning-with-errors (LWE) problem. Our protocol is in the plain model, i.e., it has no trusted setup, and it is secure in the super-polynomial simulation framework of Pass (EUROCRYPT 2003). Since two rounds are minimal for (concurrent) 2PC, this work resolves the round complexity of concurrent 2PC from standard assumptions. As immediate applications, our work establishes feasibility results for interesting cryptographic primitives, such as the first two-round password authentication key exchange (PAKE) protocol in the plain model and the first two-round concurrent secure computation protocol for quantum circuits (2PQC).
Last updated:  2023-09-22
BlindPerm: Efficient MEV Mitigation with an Encrypted Mempool and Permutation
Alireza Kavousi, Duc V. Le, Philipp Jovanovic, and George Danezis
To mitigate the negative effects of Maximal Extraction Value (MEV), we propose and explore techniques that utilize randomized permutation to shuffle the order of transactions in a committed block before they are executed. We also show that existing MEV mitigation approaches based on encrypted mempools can be extended by permutation-based techniques to provide multi-layer protection. With a focus on BFT style consensus we then propose $\textsf{BlindPerm}$, a framework enhancing an encrypted mempool with permutation at essentially no overheads and present various optimizations. Our protocol neither adds any extra latency nor requires any additional services. Finally, we demonstrate how to extend our mitigation technique to support PoW longest-chain consensus protocols.
Last updated:  2023-09-22
Sigma Protocols from Verifiable Secret Sharing and Their Applications
Min Zhang, Yu Chen, Chuanzhou Yao, and Zhichao Wang
Sigma protocols are one of the most common and efficient zero-knowledge proofs (ZKPs). Over the decades, a large number of Sigma protocols are proposed, yet few works pay attention to the common design principal. In this work, we propose a generic framework of Sigma protocols for algebraic statements from verifiable secret sharing (VSS) schemes. Our framework provides a general and unified approach to understanding Sigma protocols. It not only neatly explains the classic protocols such as Schnorr, Guillou–Quisquater and Okamoto protocols, but also leads to new Sigma protocols that were not previously known. Furthermore, we show an application of our framework in designing ZKPs for composite statements, which contain both algebraic and non-algebraic statements. We give a generic construction of non-interactive ZKPs for composite statements by combining Sigma protocols from VSS and ZKPs following MPC-in-the-head paradigm in a seamless way via a technique of \textit{witness sharing reusing}. Our construction has advantages of requiring no “glue” proofs for combining algebraic and non-algebraic statements. By instantiating our construction using Ligero++ (Bhadauria et al., CCS 2020) and designing an associated Sigma protocol from VSS, we obtain a concrete ZKP for composite statements which achieves a tradeoff between running time and proof size, thus resolving the open problem left by Backes et al. (PKC 2019).
Last updated:  2023-09-22
Rotation Key Reduction for Client-Server Systems of Deep Neural Network on Fully Homomorphic Encryption
Joon-Woo Lee, Eunsang Lee, Young-Sik Kim, and Jong-Seon No
In this paper, we propose a new concept of hierarchical rotation key for homomorphic encryption to reduce the burdens of the clients and the server running on the fully homomorphic encryption schemes such as Cheon-Kim-Kim-Song (CKKS) and Brakerski/Fan-Vercauteran (BFV) schemes. Using this concept, after the client generates and transmits only a small set of rotation keys to the server, the server can generate any required rotation keys from the public key and the smaller set of rotation keys that the client sent. This proposed method significantly reduces the communication cost of the client and the server, and the computation cost of the client. For example, if we implement the standard ResNet-18 network for the ImageNet dataset with the CKKS scheme, the server requires \numrprime{} rotation keys. It takes 145.1s for the client with a personal computer to generate whole rotation keys and the total size is 115.7GB. If we use the proposed two-level hierarchical rotation key system, the size of the rotation key set generated and transmitted by the client can be reduced from 115.7GB to 2.91GB ($\times$1/39.8), and the client-side rotation key generation runtime is reduced from 145.1s to 3.74s ($\times$38.8 faster) without any changes in any homomorphic operations to the ciphertexts. If we use the three-level hierarchical rotation key system, the size of the rotation key set generated and transmitted by the client can be further reduced from 1.54GB ($\times$1/75.1), and the client-side rotation key generation runtime is further reduced to 1.93s ($\times$75.2 faster) with a slight increase in the key-switching operation to the ciphertexts and further computation in the offline phase.
Last updated:  2023-09-22
Optimized Quantum Implementation of AES
Da Lin, Zejun Xiang, Runqing Xu, Shasha Zhang, and Xiangyong Zeng
This work researches the implementation of the AES family with Pauli-X gates, CNOT gates and Toffoli gates as the underlying quantum logic gate set. First, the properties of quantum circuits are investigated, as well as the influence of Pauli-X gates, CNOT gates and Toffoli gates on the performance of the circuits constructed with those gates. Based on these properties and the observations on the hardware circuits built by Boyar \emph{et al.} and Zou \emph{et al.}, it is possible to construct quantum circuits for AES's Substitution-box (S-box) and its inverse (S-box$^{-1}$) by rearranging the classical implementation to three parts. Since the second part is treated as a 4-bit S-box in this paper and can be dealt with by existing tools, a heuristic is proposed to search optimized quantum circuits for the first and the third parts. In addition, considering the number of parallelly executed S-boxes, the trade-offs between the qubit consumption and $T\cdot M$ values for the round function and key schedule of AES are studied. As a result, quantum circuits of AES-128, AES-192 and AES-256 can be constructed with 269, 333 and 397 qubits, respectively. If more qubits are allowed, quantum circuits that outperform state-of-the-art schemes in the metric of $T\cdot M$ value for the AES family can be reported, and it needs only 474, 538 and 602 qubits for AES-128, AES-192 and AES-256, respectively.
Last updated:  2023-09-22
Truncated Differential Attacks: New Insights and 10-round Attacks on QARMA
Zahra Ahmadian, Akram Khalesi, Dounia M'foukh, Hossein Moghimi, and María Naya-Plasencia
Truncated differential attacks were introduced by Knudsen in 1994 [1]. They are a well-known family that has arguably received less attention than some other variants of differential attacks. This paper gives some new insight on truncated differential attacks and provides the best-known attacks on both variants of the lightweight cipher QARMA, in the single tweak model, reaching for the first time 10 rounds while contradicting the security claims of this reduced version. These attacks use some new truncated distinguishers as well as some evolved key-recovery techniques.
Last updated:  2023-09-22
The supersingular endomorphism ring problem given one endomorphism
Arthur Herlédan Le Merdy and Benjamin Wesolowski
Given a supersingular elliptic curve $E$ and a non-scalar endomorphism $\alpha$ of $E$, we prove that the endomorphism ring of $E$ can be computed in classical time about $\text{disc}(\mathbb{Z}[\alpha])^{1/4}$ , and in quantum subexponential time, assuming the generalised Riemann hypothesis. Previous results either had higher complexities, or relied on heuristic assumptions. Along the way, we prove that the Primitivisation problem can be solved in polynomial time (a problem previously believed to be hard), and we prove that the action of smooth ideals on oriented elliptic curves can be computed in polynomial time (previous results of this form required the ideal to be powersmooth, i.e., not divisible by any large prime power). Following the attacks on SIDH, isogenies in high dimension are a central ingredient of our results.
Last updated:  2023-09-22
At Last! A Homomorphic AES Evaluation in Less than 30 Seconds by Means of TFHE
Daphné Trama, Pierre-Emmanuel Clet, Aymen Boudguiga, and Renaud Sirdey
Since the pioneering work of Gentry, Halevi, and Smart in 2012, the state of the art on transciphering has moved away from work on AES to focus on new symmetric algorithms that are better suited for a homomorphic execution. Yet, with recent advances in homomorphic cryptosystems, the question arises as to where we stand today. Especially since AES execution is the application that may be chosen by NIST in the FHE part of its future call for threshold encryption. In this paper, we propose an AES implementation using TFHE programmable bootstrapping which runs in less than a minute on an average laptop. We detail the transformations carried out on the original AES code to lead to a more efficient homomorphic evaluation and we also give several execution times on different machines, depending on the type of execution (sequential or parallelized). These times vary from 4.5 minutes (resp. 54 secs) for sequential (resp. parallel) execution on a standard laptop down to 28 seconds for a parallelized execution over 16 threads on a multi-core workstation.
Last updated:  2023-09-22
Practical Round-Optimal Blind Signatures in the ROM from Standard Assumptions
Shuichi Katsumata, Michael Reichle, and Yusuke Sakai
Blind signatures serve as a foundational tool for privacy-preserving applications and have recently seen renewed interest due to new applications in blockchains and privacy-authentication tokens. With this, constructing practical round-optimal (i.e., signing consists of the minimum two rounds) blind signatures in the random oracle model (ROM) has been an active area of research, where several impossibility results indicate that either the ROM or a trusted setup is inherent. In this work, we present two round-optimal blind signatures under standard assumptions in the ROM with different approaches: one achieves the smallest sum of the signature and communication sizes, while the other achieves the smallest signature size. Both of our instantiations are based on standard assumptions over asymmetric pairing groups, i.e., CDH, DDH, and/or SXDH. Our first construction is a highly optimized variant of the generic blind signature construction by Fischlin (CRYPTO'06) and has signature and communication sizes 447 B and 303 B, respectively. We progressively weaken the building blocks required by Fischlin and we result in the first blind signature where the sum of the signature and communication sizes fit below 1 KB based on standard assumptions. Our second construction is a semi-generic construction from a specific class of randomizable signature schemes that admits an all-but-one reduction. The signature size is only 96 B while the communication size is 2.2 KB. This matches the previously known smallest signature size while improving the communication size by several orders of magnitude. Finally, both of our constructions rely on a (non-black box) fine-grained analysis of the forking lemma that may be of independent interest.
Last updated:  2023-09-22
Simplified Modeling of MITM Attacks for Block Ciphers: new (Quantum) Attacks
André Schrottenloher and Marc Stevens
The meet-in-the-middle (MITM) technique has led to many key-recovery attacks on block ciphers and preimage attacks on hash functions. Nowadays, cryptographers use automatic tools that reduce the search of MITM attacks to an optimization problem. Bao et al. (EUROCRYPT 2021) introduced a low-level modeling based on Mixed Integer Linear Programming (MILP) for MITM attacks on hash functions, which was extended to key-recovery attacks by Dong et al. (CRYPTO 2021). However, the modeling only covers AES-like designs. Schrottenloher and Stevens (CRYPTO 2022) proposed a different approach aiming at higher-level simplified models. However, this modeling was limited to cryptographic permutations. In this paper, we extend the latter simplified modeling to also cover block ciphers with simple key schedules. The resulting modeling enables us to target a large array of primitives, typically lightweight SPN ciphers where the key schedule has a slow diffusion, or none at all. We give several applications such as full breaks of the PIPO-256 and FUTURE block ciphers, and reduced-round classical and quantum attacks on SATURNIN-Hash.
Last updated:  2023-09-22
HE$^3$DB: An Efficient and Elastic Encrypted Database Via Arithmetic-And-Logic Fully Homomorphic Encryption
Song Bian, Zhou Zhang, Haowen Pan, Ran Mao, Zian Zhao, Yier Jin, and Zhenyu Guan
As concerns are increasingly raised about data privacy, encrypted database management system (DBMS) based on fully homomorphic encryption (FHE) attracts increasing research attention, as FHE permits DBMS to be directly outsourced to cloud servers without revealing any plaintext data. However, the real-world deployment of FHE-based DBMS faces two main challenges: i) high computational latency, and ii) lack of elastic query processing capability, both of which stem from the inherent limitations of the underlying FHE operators. Here, we introduce HE$^3$DB, a fully homomorphically encrypted, efficient and elastic DBMS framework based on a new FHE infrastructure. By proposing and integrating new arithmetic and logic homomorphic operators, we devise fast and high-precision homomorphic comparison and aggregation algorithms that enable a variety of SQL queries to be applied over FHE ciphertexts, e.g., compound filter-aggregation, sorting, grouping, and joining. In addition, in contrast to existing encrypted DBMS that only support aggregated information retrieval, our framework permits further server-side analytical processing over the queried FHE ciphertexts, such as private decision tree evaluation. In the experiment, we rigorously study the efficiency and flexibility of HE$^3$DB. We show that, compared to the state-of-the-art techniques,HE$^3$DB can homomorphically evaluate end-to-end SQL queries as much as $41\times$ -$299\times$ faster than the state-of-the-art solution, completing a TPC-H query over a 16-bit 10K-row database within 241 seconds.
Last updated:  2023-09-22
Breaking the Size Barrier: Universal Circuits meet Lookup Tables
Yann Disser, Daniel Günther, Thomas Schneider, Maximilian Stillger, Arthur Wigandt,, and Hossein Yalame
A Universal Circuit (UC) is a Boolean circuit of size $\Theta(n \log n)$ that can simulate any Boolean function up to a certain size $n$. Valiant (STOC'76) provided the first two UC constructions of asymptotic sizes $\sim5 n\log n$ and $\sim4.75 n\log n$, and today's most efficient construction of Liu et al. (CRYPTO'21) has size $\sim3n\log n$. Evaluating a public UC with a secure Multi-Party Computation (MPC) protocol allows efficient Private Function Evaluation (PFE), where a private function is evaluated on private data. Previously, most UC constructions have only been developed for circuits consisting of 2-input gates. In this work, we generalize UCs to simulate circuits consisting of ($\rho\rightarrow\omega$)-Lookup Tables (LUTs) that map $\rho$ input bits to $\omega$ output bits. Our LUT-based UC (LUC) construction has an asymptotic size of $1.5\rho\omega n \log \omega n$ and improves the size of the UC over the best previous UC construction of Liu et al. (CRYPTO'21) by factors 1.12$\times$ - $2.18\times$ for common functions. Our results show that the greatest size improvement is achieved for $\rho=3$ inputs, and it decreases for $\rho>3$. Furthermore, we introduce Varying Universal Circuits (VUCs), which reduce circuit size at the expense of leaking the number of inputs $\rho$ and outputs $\omega$ of each LUT. Our benchmarks demonstrate that VUCs can improve over the size of the LUC construction by a factor of up to $1.45\times$.
Last updated:  2023-09-22
HEIR: A Unified Representation for Cross-Scheme Compilation of Fully Homomorphic Computation
Song Bian, Zian Zhao, Zhou Zhang, Ran Mao, Kohei Suenaga, Yier Jin, Zhenyu Guan, and Jianwei Liu
We propose a new compiler framework that automates code generation over multiple fully homomorphic encryption (FHE) schemes. While it was recently shown that algorithms combining multiple FHE schemes (e.g., CKKS and TFHE) achieve high execution efficiency and task utility at the same time, developing fast cross-scheme FHE algorithms for real-world applications generally require heavy hand-tuned optimizations by cryptographic experts, resulting in either high usability costs or low computational efficiency. To solve the usability and efficiency dilemma, we design and implement HEIR, a compiler framework based on multi-level intermediate representation (IR). To achieve cross-scheme compilation of efficient FHE circuits, we develop a two-stage code-lowering structure based on our custom IR dialects. First, the plaintext program along with the associated data types are converted into FHE-friendly dialects in the transformation stage. Then, in the optimization stage, we apply FHE-specific optimizations to lower the transformed dialect into our bottom-level FHE library operators. In the experiment, we implement the entire software stack for HEIR, and demonstrate that complex end-to-end programs, such as homomorphic K-Means clustering and homomorphic data aggregation in databases, can easily be compiled to run $72$--$179\times$ faster than the program generated by the state-of-the-art FHE compilers.
Last updated:  2023-09-22
Optimizing HE operations via Level-aware Key-switching Framework
Intak Hwang, Jinyeong Seo, and Yongsoo Song
In lattice-based Homomorphic Encryption (HE) schemes, the key-switching procedure is a core building block of non-linear operations but also a major performance bottleneck. The computational complexity of the operation is primarily determined by the so-called gadget decomposition, which transforms a ciphertext entry into a tuple of small polynomials before being multiplied with the corresponding evaluation key. However, the previous studies such as Halevi et al. (CT-RSA 2019) and Han and Ki (CT-RSA 2020) fix a decomposition function in the setup phase which is applied commonly across all ciphertext levels, resulting in suboptimal performance. In this paper, we introduce a novel key-switching framework for leveled HE schemes. We aim to allow the use of different decomposition functions during the evaluation phase so that the optimal decomposition method can be utilized at each level to achieve the best performance. A naive solution might generate multiple key-switching keys corresponding to all possible decomposition functions, and sends them to an evaluator. However, our solution can achieve the goal without such communication overhead since it allows an evaluator to dynamically derive other key-switching keys from a single key-switching key depending on the choice of gadget decomposition. We implement our framework at a proof-of-concept level to provide concrete benchmark results. Our experiments show that we achieve the optimal performance at every level while maintaining the same computational capability and communication costs.
Last updated:  2023-09-22
Asymptotically Faster Multi-Key Homomorphic Encryption from Homomorphic Gadget Decomposition
Taechan Kim, Hyesun Kwak, Dongwon Lee, Jinyeong Seo, and Yongsoo Song
Homomorphic Encryption (HE) is a cryptosytem that allows us to perform an arbitrary computation on encrypted data. The standard HE, however, has a disadvantage in that the authority is concentrated in the secret key owner since computations can only be performed on ciphertexts encrypted under the same secret key. To resolve this issue, research is underway on Multi-Key Homomorphic Encryption (MKHE), which is a variant of HE supporting computations on ciphertexts possibly encrypted under different keys. Despite its ability to provide privacy for multiple parties, existing MKHE schemes suffer from poor performance due to the cost of multiplication which grows at least quadratically with the number of keys involved. In this paper, we revisit the work of Chen et al. (ACM CCS 2019) on MKHE schemes from CKKS and BFV and significantly improve their performance. Specifically, we redesign the multi-key multiplication algorithm and achieve an asymptotically optimal complexity that grows linearly with the number of keys. Our construction relies on a new notion of gadget decomposition, which we call homomorphic gadget decomposition, where arithmetic operations can be performed over the decomposed vectors with guarantee of its functionality. Finally, we implement our MKHE schemes and demonstrate their benchmarks. For example, our multi-key CKKS multiplication takes only 0.5, 1.0, and 1.9 seconds compared to 1.6, 5.9, and 23.0 seconds of the previous work when 8, 16, and 32 keys are involved, respectively.
Last updated:  2023-09-21
Compute, but Verify: Efficient Multiparty Computation over Authenticated Inputs
Moumita Dutta, Chaya Ganesh, Sikhar Patranabis, and Nitin Singh
Traditional notions of secure multiparty computation (MPC) allow mutually distrusting parties to jointly compute a function over their private inputs, but typically do not specify how these inputs are chosen. Motivated by real-world applications where corrupt inputs could adversely impact privacy and operational legitimacy, we consider a notion of authenticated MPC where the inputs are authenticated, e.g., signed using a digital signature by some certification authority. We propose a generic and efficient compiler that transforms any linear secret sharing based honest-majority MPC protocol into one with input authentication. Our compiler incurs significantly lower computational costs and competitive communication overheads when compared to the best existing solutions, while entirely avoiding the (potentially expensive) protocol-specific techniques and pre-processing requirements that are inherent to these solutions. For $n$-party honest majority MPC protocols with abort security where each party has $\ell$ inputs, our compiler incurs $O(n\log \ell)$ communication overall and a computational overhead of $O(\ell)$ group exponentiations per party (the corresponding overheads for the most efficient existing solution are $O(n^2)$ and $O(\ell n)$). Finally, for a corruption threshold $t<n/3$, our compiler preserves the stronger identifiable abort security of the underlying MPC protocol. No existing solution for authenticated MPC achieves this regardless of the corruption threshold. Along the way, we make several technical contributions that are of independent interest. This includes the notion of distributed proofs of knowledge and concrete realizations of the same for several relations of interest, such as proving knowledge of many popularly used digital signature schemes, and proving knowledge of opening of a Pedersen commitment.
Last updated:  2023-09-21
On Time-Space Lower Bounds for Finding Short Collisions in Sponge Hash Functions
Akshima, Xiaoqi Duan, Siyao Guo, and Qipeng Liu
Sponge paradigm, used in the design of SHA-3, is an alternative hashing technique to the popular Merkle-Damgård paradigm. We revisit the problem of finding $B$-block-long collisions in sponge hash functions in the auxiliary-input random permutation model, in which an attacker gets a piece of $S$-bit advice about the random permutation and makes $T$ (forward or inverse) oracle queries to the random permutation. Recently, significant progress has been made in the Merkle-Damgård setting and optimal bounds are known for a large range of parameters, including all constant values of $B$. However, the sponge setting is widely open: there exist significant gaps between known attacks and security bounds even for $B=1$. Freitag, Ghoshal and Komargodski (CRYPTO 2022) showed a novel attack for $B=1$ that takes advantage of the inverse queries and achieves advantage $\tilde{\Omega}(\min(S^2T^2/2^{2c}$, $ (S^2T/2^{2c})^{2/3})+T^2/2^r)$, where $r$ is bit-rate and $c$ is the capacity of the random permutation. However, they only showed an $\tilde{O}(ST/2^c+T^2/2^r)$ security bound, leaving open an intriguing quadratic gap. For $B=2$, they beat the general security bound by Coretti, Dodis, Guo (CRYPTO 2018) for arbitrary values of $B$. However, their highly non-trivial argument is quite laborious, and no better (than the general) bounds are known for $B\geq 3$. In this work, we study the possibility of proving better security bounds in the sponge setting. To this end, - For $B=1$, we prove an improved $\tilde{O}(S^2T^2/2^{2c}+S/2^c+T/2^c+T^2/2^r)$ bound. Our bound strictly improves the bound by Freitag et al., and is optimal for $ST^2\leq 2^c$. - For $B=2$, we give a considerably simpler and more modular proof, recovering the bound obtained by Freitag et al. - We obtain our bounds by adapting the recent multi-instance technique of Akshima, Guo and Liu (CRYPTO 2022) which bypasses the limitations of prior techniques in the Merkle-Damgård setting. To complement our results, we provably show that the recent multi-instance technique cannot further improve our bounds for $B=1,2$, and the general bound by Correti et al., for $B\geq 3$. Overall, our results yield state-of-the-art security bounds for finding short collisions and fully characterize the power of the multi-instance technique in the sponge setting.
Last updated:  2023-09-21
Anonymous Permutation Routing
Paul Bunn, Eyal Kushilevitz, and Rafail Ostrovsky
The Non-Interactive Anonymous Router (NIAR) model was introduced by Shi and Wu [SW21] as an alternative to conventional solutions to the anonymous routing problem, in which a set of senders wish to send messages to a set of receivers. In contrast to most known approaches to support anonymous routing (e.g. mix-nets, DC-nets, etc.) which rely on a network of routers communicating with users via interactive protocols, the NIAR model assumes a $single$ router and is inherently $non$-$interactive$ (after an initial setup phase). In addition to being non-interactive, the NIAR model is compelling due to the security it provides: instead of relying on the honesty of some subset of the routers, the NIAR model requires anonymity even if the router (as well as an arbitrary subset of senders/receivers) is corrupted. In this paper, we present a protocol for the NIAR model that improves upon the results from [SW21] in two ways: - Improved computational efficiency (quadratic to near linear): Our protocol matches the communication complexity of [SW21] for each sender/receiver, while reducing the computational overhead for the router to polylog overhead instead of linear overhead. - Relaxation of assumptions: Security of the protocol in [SW21] relies on the Decisional Linear assumption in bilinear groups; while security for our protocol follows from the existence of any rate-1 oblivious transfer (OT) protocol (instantiations of this primitive are known to exist under DDH, QR and LWE [DGI19,GHO20]).
Last updated:  2023-09-21
Security with Functional Re-Encryption from CPA
Yevgeniy Dodis, Shai Halevi, and Daniel Wichs
The notion of functional re-encryption security (funcCPA) for public-key encryption schemes was recently introduced by Akavia et al. (TCC'22), in the context of homomorphic encryption. This notion lies in between CPA security and CCA security: we give the attacker a functional re-encryption oracle instead of the decryption oracle of CCA security. This oracle takes a ciphertext $c$ and a function $f$, and returns fresh encryption of the output of $f$ applied to the decryption of $c$; in symbols, $c'=Enc(f(Dec(c)))$. More generally, we even allow for a multi-input version, where the oracle takes an arbitrary number of ciphetexts $c_1,\ldots,c_\ell$ and outputs $c' = Enc(f(Dec(c_1), \ldots, Dec(c_\ell)))$. In this work we observe that funcCPA security may have applications beyond homomorphic encryption, and set out to study its properties. As our main contribution, we prove that funcCPA is ``closer to CPA than to CCA''; that is, funcCPA secure encryption can be constructed in a black-box manner from CPA-secure encryption. We stress that, prior to our work, this was not known even for basic re-encryption queries corresponding to the identity function $f$. At the core of our result is a new technique, showing how to handle adaptive functional re-encryption queries using tools previously developed in the context of non-malleable encryption, which roughly corresponds to a single non-adaptive parallel decryption query.
Last updated:  2023-09-21
Advanced Composition Theorems for Differential Obliviousness
Mingxun Zhou, Mengshi Zhao, T-H. Hubert Chan, and Elaine Shi
Differential obliviousness (DO) is a privacy notion which mandates that the access patterns of a program satisfy differential privacy. Earlier works have shown that in numerous applications, differential obliviousness allows us to circumvent fundamental barriers pertaining to fully oblivious algorithms, resulting in asymptotical (and sometimes even polynomial) performance improvements. Although DO has been applied to various contexts, including the design of algorithms, data structures, and protocols, its compositional properties are not explored until the recent work of Zhou et al. (Eurocrypt'23). Specifically, Zhou et al. showed that the original DO notion is not composable. They then proposed a refinement of DO called neighbor-preserving differential obliviousness (NPDO), and proved a basic composition for NPDO. In Zhou et al.'s basic composition theorem for NPDO, the privacy loss is linear in $k$ for $k$-fold composition. In comparison, for standard differential privacy, we can enjoy roughly $\sqrt{k}$ loss for $k$-fold composition by applying the well-known advanced composition theorem. Therefore, a natural question left open by their work is whether we can also prove an analogous advanced composition for NPDO. In this paper, we answer this question affirmatively. As a key step in proving an advanced composition theorem for NPDO, we define a more operational notion called symmetric NPDO which we prove to be equivalent to NPDO. Using symmetric NPDO as a stepping stone, we also show how to generalize NPDO to more general notions of divergence, resulting in Rényi-NPDO, zero-concentrated NPDO, Gassian-NPDO, and $g$-NPDO notions. We also prove composition theorems for these generalized notions of NPDO.
Last updated:  2023-09-21
A Theory of Composition for Differential Obliviousness
Mingxun Zhou, Elaine Shi, T-H. Hubert Chan, and Shir Maimon
Differential obliviousness (DO) access pattern privacy is a privacy notion which guarantees that the access patterns of a program satisfy differential privacy. Differential obliviousness was studied in a sequence of recent works as a relaxation of full obliviousness. Earlier works showed that DO not only allows us to circumvent the logarithmic-overhead barrier of fully oblivious algorithms, in many cases, it also allows us to achieve polynomial speedup over full obliviousness, since it avoids "padding to the worst-case" behavior of fully oblivious algorithms. Despite the promises of differential obliviousness (DO), a significant barrier that hinders its broad application is the lack of composability. In particular, when we apply one DO algorithm to the output of another DO algorithm, the composed algorithm may no longer be DO (with reasonable parameters). More specifically, the outputs of the first DO algorithm on two neighboring inputs may no longer be neighboring, and thus we cannot directly benefit from the DO guarantee of the second algorithm. In this work, we are the first to explore a theory of composition for differentially oblivious algorithms. We propose a refinement of the DO notion called $(\epsilon, \delta)$-neighbor-preserving-DO, or $(\epsilon, \delta)$-NPDO for short, and we prove that our new notion indeed provides nice compositional guarantees. In this way, the algorithm designer can easily track the privacy loss when composing multiple DO algorithms. We give several example applications to showcase the power and expressiveness of our new NPDO notion. One of these examples is a result of independent interest: we use the compositional framework to prove an optimal privacy amplification theorem for the differentially oblivious shuffle model. In other words, we show that for a class of distributed differentially private mechanisms in the shuffle-model, one can replace the perfectly secure shuffler with a DO shuffler, and nonetheless enjoy almost the same privacy amplification enabled by a shuffler.
Last updated:  2023-09-21
Everlasting ROBOT: the Marvin Attack
Hubert Kario
In this paper we show that Bleichenbacher-style attacks on RSA decryption are not only still possible, but also that vulnerable implementations are common. We have successfully attacked multiple implementations using only timing of decryption operation and shown that many others are vulnerable. To perform the attack we used more statistically rigorous techniques like the sign test, Wilcoxon signed-rank test, and bootstrapping of median of pairwise differences. We publish a set of tools for testing libraries that perform RSA decryption against timing side-channel attacks, including one that can test arbitrary TLS servers with no need to write a test harnesses. Finally, we propose a set of workarounds that implementations can employ if they can't avoid the use of RSA.
Last updated:  2023-09-21
Out of the Box Testing
Hubert Kario
In this paper we analyse typical timing data that can be collected over loopback interface, in local, and in metropolitan area networks. We evaluate performance of few statistical test for detecting differences in timing of server responses. The evaluated tests include the popular Box test, as well as sign test, Wilcoxon signed-rank test, and paired sample t-test. We found that the Box test offers poor performance, as it's an incorrect test to use for the measurements we collected. Use of appropriate tests also allows for robust differentiation between much smaller differences than the existing literature would suggest. We were able to detect side channels of single-digit CPU cycles over regular gigabit Ethernet. Those alternative tests were also found to be robust against noise in production networks, allowing detection of side channel of just few nanoseconds with 6 network hops between test systems.
Last updated:  2023-09-21
Near-Optimal Private Information Retrieval with Preprocessing
Arthur Lazzaretti and Charalampos Papamanthou
In Private Information Retrieval (PIR), a client wishes to access an index $i$ from a public $n$-bit database without revealing any information about $i$. Recently, a series of works starting with the seminal paper of Corrigan-Gibbs and Kogan (EUROCRYPT 2020) considered PIR with \emph{client preprocessing} and \emph{no additional server storage}. In this setting, we now have protocols that achieve $\widetilde{O}(\sqrt{n})$ (amortized) server time and $\widetilde{O}(1)$ (amortized) bandwidth in the two-server model (Shi et al., CRYPTO 2021) as well as $\widetilde{O}(\sqrt{n})$ server time and $\widetilde{O}(\sqrt{n})$ bandwidth in the single-server model (Corrigan-Gibbs et al., EUROCRYPT 2022). Given existing lower bounds, a single-server PIR scheme with $\widetilde{O}(\sqrt{n})$ (amortized) server time and $\widetilde{O}(1)$ (amortized) bandwidth is still feasible, however, to date, no known protocol achieves such complexities. In this paper we fill this gap by constructing the first single-server PIR scheme with $\widetilde{O}(\sqrt{n})$ (amortized) server time and $\widetilde{O}(1)$ (amortized) bandwidth. Our scheme achieves near-optimal (optimal up to polylogarithmic factors) asymptotics in every relevant dimension. Central to our approach is a new cryptographic primitive that we call an adaptable pseudorandom set: With an adaptable pseudorandom set, one can represent a large pseudorandom set with a succinct fixed-size key $k$, and can both add to and remove from the set a constant number of elements by manipulating the key $k$, while maintaining its concise description as well as its pseudorandomness (under a certain security definition).
Last updated:  2023-09-21
Comment on Enhanced DNA and ElGamal cryptosystem for secure data storage and retrieval in cloud
Chenglian Liu and Sonia Chien-I Chen
Thangavel and Varalakshmi proposed an enhanced DNA and ElGamal cryptosystem for secure data storage and retrieval in cloud. They modified ElGamal algorithm which it calls enhanced ElGamal cryptosystem. We prove that their enhanced ElGamal scheme, which does not require two random numbers by data owner. Although the attacker is unable to find out what message the data owner gave to the data user. However, the attackers can still confuse the issue of sending messages to data users. On the other hand, this scheme can not against insider attack, therefore it is insecure.
Last updated:  2023-09-21
Dynamic Security Aspects of Onion Routing
Alessandro Melloni, Martijn Stam, and Øyvind Ytrehus
An anonymous communication network (ACN) is designed to protect the identities of two parties communicating through it, even if an adversary controls or observes parts of the network. Among the ACNs, Tor represents a practical trade-off between offering a reasonable level of anonymity and, simultaneously, an acceptable transmission delay. Due to its practical impact, there is abundant literature on the performance of Tor concerning both communication and security aspects. Recently, a static framework was suggested for evaluating and comparing, in a quantifiable way, the effect of different scenarios (attacks, defence mechanisms, and other protocol changes). Although a static model is useful, many scenarios involve parameters and stochastic variables that change or evolve over time, or that may be influenced by active and malicious adversaries. In this paper, we propose a dynamic framework for evaluating such scenarios. We identify several scenarios where this framework is applicable, and illustrate our framework by considering the guard node mechanism in Tor. We evaluate and compare variations on the guard node concept suggested in the literature with respect to relevant performance metrics and, using the framework, support our evaluation with a theoretical analysis.
Last updated:  2023-09-21
Batch point compression in the context of advanced pairing-based protocols
Dmitrii Koshelev
This paper continues previous ones about compression of points on elliptic curves $E_b\!: y^2 = x^3 + b$ (with $j$-invariant $0$) over a finite field $\mathbb{F}_{\!q}$ of characteristic $p > 3$. It is shown in detail how any two (resp., three) points from $E_b(\mathbb{F}_{\!q})$ can be quickly compressed to two (resp., three) elements of $\mathbb{F}_{\!q}$ (apart from a few auxiliary bits) in such a way that the corresponding decompression stage requires to extract only one cubic (resp., sextic) root in $\mathbb{F}_{\!q}$. As a result, for many fields $\mathbb{F}_{\!q}$ occurring in practice, the new compression-decompression methods are more efficient than the classical one with the two (resp., three) $x$ or $y$ coordinates of the points, which extracts two (resp., three) roots in $\mathbb{F}_{\!q}$. As a by-product, it is also explained how to sample uniformly at random two (resp., three) ``independent'' $\mathbb{F}_{\!q}$-points on $E_b$ essentially at the cost of only one cubic (resp., sextic) root in $\mathbb{F}_{\!q}$. Finally, the cases of four and more points from $E_b(\mathbb{F}_{\!q})$ are commented on as well.
Last updated:  2023-09-21
A New Formulation of the Linear Equivalence Problem and Shorter LESS Signatures
Edoardo Persichetti and Paolo Santini
The Linear Equivalence Problem (LEP) asks to find a linear isometry between a given pair of linear codes; in the Hamming weight this is known as a monomial map. LEP has been used in cryptography to design the family of LESS signatures, which includes also some advanced schemes, such as ring and identity-based signatures. All of these schemes are obtained applying the Fiat-Shamir transformation to a Sigma protocol, in which the prover's responses contain a description of how the monomial map acts on all code coordinates; such a description constitutes the vast majority of the signature size. In this paper, we propose a new formulation of LEP, which we refer to as Information-Set (IS)-LEP. Exploiting IS-LEP, it is enough for the prover to provide the description of the monomial action only on an information set, instead of all the coordinates. Thanks to this new formulation, we are able to drastically reduce signature sizes for all LESS signature schemes, without any relevant computational overhead. We prove that IS-LEP and LEP are completely equivalent (indeed, the same problem), which means that improvement comes with no additional security assumption, either.
Last updated:  2023-09-21
Trivial Transciphering With Trivium and TFHE
Thibault Balenbois, Jean-Baptiste Orfila, and Nigel P. Smart
We examine the use of Trivium and Kreyvium as transciphering mechanisms for use with the TFHE FHE scheme. Originally these two ciphers were investigated for FHE transciphering only in the context of the BGV/BFV FHE schemes; this is despite Trivium and Kreyvium being particarly suited to TFHE. Recent work by Dobraunig et al. gave some initial experimental results using TFHE. We show that these two symmetric ciphers have excellent performance when homomorphically evaluated using TFHE. Indeed we improve upon the results of Dobraunig et al. by at least two orders of magnitude in terms of latency. This shows that, for TFHE at least, one can transcipher using a standardized symmetric cipher (Trivium), without the need for special FHE-friendly ciphers being employed. For applications wanting extra security, but without the benefit of relying on a standardized cipher, our work shows that Kreyvium is a good candidate.
Last updated:  2023-09-21
Toward Practical Lattice-based Proof of Knowledge from Hint-MLWE
Duhyeong Kim, Dongwon Lee, Jinyeong Seo, and Yongsoo Song
In the last decade, zero-knowledge proof of knowledge protocols have been extensively studied to achieve active security of various cryptographic protocols. However, the existing solutions simply seek zero-knowledge for both message and randomness, which is an overkill in many applications since protocols may remain secure even if some information about randomness is leaked to the adversary. We develop this idea to improve the state-of-the-art proof of knowledge protocols for RLWE-based public-key encryption and BDLOP commitment schemes. In a nutshell, we present new proof of knowledge protocols without using noise flooding or rejection sampling which are provably secure under a computational hardness assumption, called Hint-MLWE. We also show an efficient reduction from Hint-MLWE to the standard MLWE assumption. Our approach enjoys the best of two worlds because it has no computational overhead from repetition (abort) and achieves a polynomial overhead between the honest and proven languages. We prove this claim by demonstrating concrete parameters and compare with previous results. Finally, we explain how our idea can be further applied to other proof of knowledge providing advanced functionality.
Last updated:  2023-09-21
Quantum Analysis of AES
Kyungbae Jang, Anubhab Baksi, Hyunji Kim, Gyeongju Song, Hwajeong Seo, and Anupam Chattopadhyay
Quantum computing is considered among the next big leaps in computer science. While a fully functional quantum computer is still in the future, there is an ever-growing need to evaluate the security of the secret-key ciphers against a potent quantum adversary. Keeping this in mind, our work explores the key recovery attack using the Grover's search on the three variants of AES (-128, -192, -256). In total, we develop a pool of 14 implementations per AES variant, by taking the state-of-the-art advancements in the relevant fields into account. In a nutshell, we present the least Toffoli depth and full depth implementations of AES, thereby improving from Zou et al.'s Asiacrypt'20 paper by more than 98 percent for all variants of AES. We show that the qubit count - Toffoli depth product is reduced from theirs by more than 75 percent. Furthermore, we analyze the Jaques et al.'s Eurocrypt'20 implementations in details, fix the bugs (arising from some problem of the quantum computing tool used and not related to their coding) and report corrected benchmarks. To the best of our finding, our work improves from all the previous works (including the Asiacrypt'22 paper by Huang and Sun) in terms of various quantum circuit complexity metrics (such as, Toffoli depth, full depth, Toffoli depth - qubit count product, and so on). Equipped with the basic AES implementations, we further investigate the prospect of the Grover's search. In that direction, under the MAXDEPTH constraint (specified by NIST), the circuit depth metrics (Toffoli depth, T-depth and full depth) become crucial factors and parallelization for often becomes necessary. We provide the least depth implementation in this respect, that offers the best performance in terms of metrics for circuit complexity (like, depth-squared - gate count product, depth-squared - qubit count product).
Last updated:  2023-09-21
Simple Threshold (Fully Homomorphic) Encryption From LWE With Polynomial Modulus
Katharina Boudgoust and Peter Scholl
The learning with errors (LWE) assumption is a powerful tool for building encryption schemes with useful properties, such as plausible resistance to quantum computers, or support for homomorphic computations. Despite this, essentially the only method of achieving threshold decryption in schemes based on LWE requires a modulus that is superpolynomial in the security parameter, leading to a large overhead in ciphertext sizes and computation time. In this work, we propose a (fully homomorphic) encryption scheme that supports a simple $t$-out-of-$n$ threshold decryption protocol while allowing for a polynomial modulus. The main idea is to use the Rényi divergence (as opposed to the statistical distance as in previous works) as a measure of distribution closeness. This comes with some technical obstacles, due to the difficulty of using the Rényi divergence in decisional security notions such as standard semantic security. We overcome this by constructing a threshold scheme with a weaker notion of one-way security and then showing how to transform any one-way threshold scheme into one guaranteeing indistinguishability-based security.
Last updated:  2023-09-21
Private Web Search with Tiptoe
Alexandra Henzinger, Emma Dauterman, Henry Corrigan-Gibbs, and Nickolai Zeldovich
Tiptoe is a private web search engine that allows clients to search over hundreds of millions of documents, while revealing no information about their search query to the search engine’s servers. Tiptoe’s privacy guarantee is based on cryptography alone; it does not require hardware enclaves or non-colluding servers. Tiptoe uses semantic embeddings to reduce the problem of private full-text search to private nearest-neighbor search. Then, Tiptoe implements private nearest-neighbor search with a new, high-throughput protocol based on linearly homomorphic encryption. Running on a 45-server cluster, Tiptoe can privately search over 360 million web pages with 145 core-seconds of server compute, 56.9 MiB of client-server communication (74% of which occurs before the client enters its search query), and 2.7 seconds of end-to-end latency. Tiptoe’s search works best on conceptual queries (“knee pain”) and less well on exact string matches (“123 Main Street, New York”). On the MS MARCO search-quality benchmark, Tiptoe ranks the best-matching result in position 7.7 on average. This is worse than a state-of-the-art, non-private neural search algorithm (average rank: 2.3), but is close to the classical tf-idf algorithm (average rank: 6.7). Finally, Tiptoe is extensible: it also supports private text-to-image search and, with minor modifications, it can search over audio, code, and more.
Last updated:  2023-09-21
Concurrent Security of Anonymous Credentials Light, Revisited
Julia Kastner, Julian Loss, and Omar Renawi
We revisit the concurrent security guarantees of the well-known Anonymous Credentials Light (ACL) scheme (Baldimtsi and Lysyanskaya, CCS'13). This scheme was originally proven secure when executed sequentially, and its concurrent security was left as an open problem. A later work of Benhamouda et al. (EUROCRYPT'21) gave an efficient attack on ACL when executed concurrently, seemingly resolving this question once and for all. In this work, we point out a subtle flaw in the attack of Benhamouda et al. on ACL and show, in spite of popular opinion, that it can be proven concurrently secure. Our modular proof in the algebraic group model uses an ID scheme as an intermediate step and leads to a major simplification of the complex security argument for Abe's Blind Signature scheme by Kastner et al. (PKC'22).
Last updated:  2023-09-21
Cryptanalysis of Elisabeth-4
Henri Gilbert, Rachelle Heim Boissier, Jérémy Jean, and Jean-René Reinhard
Elisabeth-4 is a stream cipher tailored for usage in hybrid homomorphic encryption applications that has been introduced by Cosseron et al. at ASIACRYPT 2022. In this paper, we present several variants of a key-recovery attack on the full Elisabeth-4 that break the 128-bit security claim of that cipher. Our most optimized attack is a chosen-IV attack with a time complexity of $2^{88}$ elementary operations, a memory complexity of $2^{54}$ bits and a data complexity of $2^{41}$ bits. Our attack applies the linearization technique to a nonlinear system of equations relating some keystream bits to the key bits and exploits specificities of the cipher to solve the resulting linear system efficiently. First, due to the structure of the cipher, the system to solve happens to be very sparse, which enables to rely on sparse linear algebra and most notably on the Block Wiedemann algorithm. Secondly, the algebraic properties of the two nonlinear ingredients of the filtering function cause rank defects which can be leveraged to solve the linearized system more efficiently with a decreased data and time complexity. We have implemented our attack on a toy version of Elisabeth-4 to verify its correctness. It uses the efficient implementation of the Block Wiedemann algorithm of CADO-NFS for the sparse linear algebra.
Last updated:  2023-09-21
Threshold Structure-Preserving Signatures
Elizabeth Crites, Markulf Kohlweiss, Bart Preneel, Mahdi Sedaghat, and Daniel Slamanig
Structure-preserving signatures (SPS) are an important building block for privacy-preserving cryptographic primitives, such as electronic cash, anonymous credentials, and delegatable anonymous credentials. In this work, we introduce the first threshold structure-preserving signature scheme (TSPS). This enables multiple parties to jointly sign a message, resulting in a standard, single-party SPS signature, and can thus be used as a replacement for applications based on SPS. We begin by defining and constructing SPS for indexed messages, which are messages defined relative to a unique index. We prove its security in the random oracle model under a variant of the generalized Pointcheval-Sanders assumption (PS). Moreover, we generalize this scheme to an indexed multi-message SPS for signing vectors of indexed messages, which we prove secure under the same assumption. We then formally define the notion of a TSPS and propose a construction based on our indexed multi-message SPS. Our TSPS construction is fully non-interactive, meaning that signers simply output partial signatures without communicating with the other signers. Additionally, signatures are short: they consist of 2 group elements and require 2 pairing product equations to verify. We prove the security of our TSPS under the security of our indexed multi-message SPS scheme. Finally, we show that our TSPS may be used as a drop-in replacement for UC-secure Threshold-Issuance Anonymous Credential (TIAC) schemes, such as Coconut, without the overhead of the Fischlin transform.
Last updated:  2023-09-21
More Balanced Polynomials: Cube Attacks on 810- and 825-Round Trivium with Practical Complexities
Hao Lei, Jiahui He, Kai Hu, and Meiqin Wang
The key step of the cube attack is to recover the special polynomial, the superpoly, of the target cipher. In particular, the balanced superpoly, in which there exists at least one secret variable as a single monomial and none of the other monomials contain this variable, can be exploited to reveal one-bit information about the key bits. However, as the number of rounds grows, it becomes increasingly difficult to find such balanced superpolies. Consequently, traditional methods of searching for balanced superpolies soon hit a bottleneck. Aiming at performing a cube attack on more rounds of Trivium with a practical complexity, in this paper, we present three techniques to obtain sufficient balanced polynomials. 1. Based on the structure of Trivium, we propose a variable substitution technique to simplify the superpoly. 2. Obtaining the additional balanced polynomial by combining two superpolies to cancel the two-degree terms. 3. We propose an experimental approach to construct high-quality large cubes which may contain more subcubes with balanced superpolies and a heuristic search strategy for their subcubes whose superpolies are balanced. To illustrate the power of our techniques, we search for balanced polynomials for 810- and 825-round Trivium. As a result, we can mount cube attacks against 810- and 825-round Trivium with the time complexity of $2^{44.17}$ and $2^{53.17}$ round-reduced Trivium initializations, respectively, which can be verified in 48 minutes and 18 days on a PC with one A100 GPU. For the same level of time complexity, this improves the previous best results by $2$ and $5$ rounds, respectively.
Last updated:  2023-09-21
Identity-Based Matchmaking Encryption, Revisited: Strong Security and Practical Constructions from Standard Classical and Post-Quantum Assumptions
Sohto Chiku, Keitaro Hashimoto, Keisuke Hara, and Junji Shikata
Identity-based matchmaking encryption (IB-ME), proposed by Ateniese et al. at Crypto 2019, allows users to communicate privately in an anonymous and authenticated manner. In this work, we revisit the security definitions and construction of IB-ME. First, we re-formalize the existing security notions for IB-ME. We reorganize privacy and authenticity notions into respective three and four definitions, which allows us to compare IB-ME schemes accurately. Second, we propose a highly efficient and strongly secure IB-ME scheme from the bilinear Diffie-Hellman assumption in the random oracle model. This scheme is based on the IB-ME scheme proposed by Ateniese et al., but we introduce several techniques to improve its security and efficiency. Third, we propose a new generic construction of IB-ME from anonymous identity-based encryption and identity-based signature. This is the first generic construction that does not rely on hierarchical identity-based encryption. Through this construction, we obtain various IB-ME schemes from both classical and post-quantum assumptions. For example, we obtain a more efficient scheme from the symmetric external Diffie-Hellman assumption in the standard model, and a practical scheme from lattices in the quantum random oracle model whose secret keys and ciphertexts are less than 10 Kilobytes. Moreover, our generic construction produces the first pairing-free IB-ME scheme in the standard model and the first tightly secure lattice-based IB-ME scheme in the quantum random oracle model.
Last updated:  2023-09-21
Public-Key Encryption with Quantum Keys
Khashayar Barooti, Alex B. Grilo, Loïs Huguenin-Dumittan, Giulio Malavolta, Or Sattath, Quoc-Huy Vu, and Michael Walter
In the framework of Impagliazzo's five worlds, a distinction is often made between two worlds, one where public-key encryption exists (Cryptomania), and one in which only one-way functions exist (MiniCrypt). However, the boundaries between these worlds can change when quantum information is taken into account. Recent work has shown that quantum variants of oblivious transfer and multi-party computation, both primitives that are classically in Cryptomania, can be constructed from one-way functions, placing them in the realm of quantum MiniCrypt (the so-called MiniQCrypt). This naturally raises the following question: Is it possible to construct a quantum variant of public-key encryption, which is at the heart of Cryptomania, from one-way functions or potentially weaker assumptions? In this work, we initiate the formal study of the notion of quantum public-key encryption (qPKE), i.e., public-key encryption where keys are allowed to be quantum states. We propose new definitions of security and several constructions of qPKE based on the existence of one-way functions (OWF), or even weaker assumptions, such as pseudorandom function-like states (PRFS) and pseudorandom function-like states with proof of destruction (PRFSPD). Finally, to give a tight characterization of this primitive, we show that computational assumptions are necessary to build quantum public-key encryption. That is, we give a self-contained proof that no quantum public-key encryption scheme can provide information-theoretic security.
Last updated:  2023-09-21
An Efficient Strong Asymmetric PAKE Compiler Instantiable from Group Actions
Ian McQuoid and Jiayu Xu
Password-authenticated key exchange (PAKE) is a class of protocols enabling two parties to convert a shared (possibly low-entropy) password into a high-entropy joint session key. Strong asymmetric PAKE (saPAKE), an extension that models the client-server setting where servers may store a client's password for repeated authentication, was the subject of standardization efforts by the IETF in 2019-20. In this work, we present the most computationally efficient saPAKE protocol so far: a compiler from PAKE to saPAKE which costs only 2 messages and 7 group exponentiations in total (3 for client and 4 for server) when instantiated with suitable underlying PAKE protocols. In addition to being efficient, our saPAKE protocol is conceptually simple and achieves the strongest notion of universally composable (UC) security. In addition to classical assumptions and classical PAKE, we may instantiate our PAKE-to-saPAKE compiler with cryptographic group actions, such as the isogeny-based CSIDH, and post-quantum PAKE. This yields the first saPAKE protocol from post-quantum assumptions as all previous constructions rely on cryptographic assumptions weak to Shor's algorithm.
Last updated:  2023-09-21
FESTA: Fast Encryption from Supersingular Torsion Attacks
Andrea Basso, Luciano Maino, and Giacomo Pope
We introduce FESTA, an efficient isogeny-based public-key encryption (PKE) protocol based on a constructive application of the SIDH attacks. At its core, FESTA is based on a novel trapdoor function, which uses an improved version of the techniques proposed in the SIDH attacks to develop a trapdoor mechanism. Using standard transformations, we construct an efficient PKE that is IND-CCA secure in the QROM. Additionally, using a different transformation, we obtain the first isogeny-based PKE that is IND-CCA secure in the standard model. Lastly, we propose a method to efficiently find parameters for FESTA, and we develop a proof-of-concept implementation of the protocol. We expect FESTA to offer practical performance that is competitive with existing isogeny-based constructions.
Last updated:  2023-09-21
A polynomial-time attack on instances of M-SIDH and FESTA
Wouter Castryck and Frederik Vercauteren
The recent devastating attacks on SIDH rely on the fact that the protocol reveals the images $\varphi(P)$ and $\varphi(Q)$ of the secret isogeny $\varphi : E_0 \rightarrow E$ on a basis $\{P, Q\}$ of the $N$-torsion subgroup $E_0[N]$ where $N^2 > \deg(\varphi)$. To thwart this attack, two recent proposals, M-SIDH and FESTA, proceed by only revealing the images upto unknown scalars $\lambda_1, \lambda_2 \in \mathbb{Z}_N^\times$, i.e., only $\lambda_1 \varphi(P)$ and $\lambda_2 \varphi(Q)$ are revealed, where $\lambda_1 = \lambda_2$ for M-SIDH and $\lambda_1 = \lambda_2^{-1}$ for FESTA. Similar information is leaked in CSIDH since $\varphi$ maps the eigenspaces of Frobenius on $E_0$ to the corresponding eigenspaces on $E$. In this paper, we introduce a new polynomial time attack that generalizes the well known "lollipop" attack and analyze how it applies to M-SIDH, FESTA and CSIDH. We show that M-SIDH can be broken in polynomial time whenever $E_0$ or $E$ is $\mathbb{F}_p$-rational, even when the endomorphism rings of $E_0$ and $E$ are unknown. This can be generalized to the case where the starting (or end) curve is not $\mathbb{F}_p$-rational, but is connected to its Frobenius conjugate by an isogeny of small degree. For FESTA, where the curve $E_0$ is already $\mathbb{F}_p$-rational, we obtain a polynomial time attack under the added requirement that at least one of the basis points $P, Q$ spans an eigenspace of Frobenius, of an endomorphism of low degree, or of a composition of both. We note that the current implementation of FESTA does not choose such a basis. Since it is always possible to construct an endomorphism, typically of large degree, with either $P, Q$ an eigenvector, we conclude that FESTA with overstretched parameters is insecure. Although the information leaked in CSIDH is very similar to FESTA, we show that our attack does not reveal any new information about the secret isogeny, i.e., we only learn that it is $\mathbb{F}_p$-rational, which is a priori knowledge. Finally, we analyze if and how it would be possible to backdoor M-SIDH and FESTA by choosing system parameters that look inconspicuous, but in fact reduce to the special cases above via a secret isogeny chosen by the adversary.
Last updated:  2023-09-21
Populating the Zoo of Rugged Pseudorandom Permutations
Jean Paul Degabriele and Vukašin Karadžić
A Rugged Pseudorandom Permutation (RPRP) is a variable-input-length tweakable cipher satisfying a security notion that is intermediate between tweakable PRP and tweakable SPRP. It was introduced at CRYPTO 2022 by Degabriele and Karadžić, who additionally showed how to generically convert such a primitive into nonce-based and nonce-hiding AEAD schemes satisfying either misuse-resistance or release-of-unverified-plaintext security as well as Nonce-Set AEAD which has applications in protocols like QUIC and DTLS. Their work shows that RPRPs are powerful and versatile cryptographic primitives. However, the RPRP security notion itself can seem rather contrived, and the motivation behind it is not immediately clear. Moreover, they only provided a single RPRP construction, called UIV, which puts into question the generality of their modular approach and whether other instantiations are even possible. In this work, we address this question positively by presenting new RPRP constructions, thereby validating their modular approach and providing further justification in support of the RPRP security definition. Furthermore, we present a more refined view of their results by showing that strictly weaker RPRP variants, which we introduce, suffice for many of their transformations. From a theoretical perspective, our results show that the well-known three-round Feistel structure achieves stronger security as a permutation than a mere pseudorandom permutation---as was established in the seminal result by Luby and Rackoff. We conclude on a more practical note by showing how to extend the left domain of one RPRP construction for applications that require larger values in order to meet the desired level of security.
Last updated:  2023-09-21
Forgery Attacks on Several Beyond-Birthday-Bound Secure MACs
Yaobin Shen, François-Xavier Standaert, and Lei Wang
At CRYPTO'18, Datta et al. proposed nPolyMAC and proved the security up to 2^{2n/3} authentication queries and 2^{n} verification queries. At EUROCRYPT'19, Dutta et al. proposed CWC+ and showed the security up to 2^{2n/3} queries. At FSE'19, Datta et al. proposed PolyMAC and its key-reduced variant 2k-PolyMAC, and showed the security up to 2^{2n/3} queries. This security bound was then improved by Kim et al. (EUROCRYPT'20) and Datta et al (FSE'23) respectively to 2^{3n/4} and in the multi-user setting. At FSE'20, Chakraborti et al. proposed PDM*MAC and 1k-PDM*MAC and showed the security up to 2^{2n/3} queries. Recently, Chen et al. proposed nEHtM_p^+ and showed the security up to 2^{2n/3} queries. In this paper, we show forgery attacks on nPolyMAC, CWC+, PolyMAC, 2k-PolyMAC, PDM*MAC, 1k-PDM*MAC and nEHtM_p^+. Our attacks exploit some vulnerability in the underlying polynomial hash function Poly, and (i) require only one authentication query and one verification query; (ii) are nonce-respecting; (iii) succeed with probability 1. Thus, our attacks disprove the provable high security claims of these schemes. We then revisit their security analyses and identify what went wrong. Finally, we propose two solutions that can restore the beyond-birthday-bound security.
Last updated:  2023-09-21
One-out-of-Many Unclonable Cryptography: Definitions, Constructions, and More
Fuyuki Kitagawa and Ryo Nishimaki
The no-cloning principle of quantum mechanics enables us to achieve amazing unclonable cryptographic primitives, which is impossible in classical cryptography. However, the security definitions for unclonable cryptography are tricky. Achieving desirable security notions for unclonability is a challenging task. In particular, there is no indistinguishable-secure unclonable encryption and quantum copy-protection for single-bit output point functions in the standard model. To tackle this problem, we introduce and study relaxed but meaningful security notions for unclonable cryptography in this work. We call the new security notion one-out-of-many unclonable security. We obtain the following results. - We show that one-time strong anti-piracy secure secret key single-decryptor encryption (SDE) implies one-out-of-many indistinguishable-secure unclonable encryption. - We construct a one-time strong anti-piracy secure secret key SDE scheme in the standard model from the LWE assumption. - We construct one-out-of-many copy-protection for single-bit output point functions from one-out-of-many indistinguishable-secure unclonable encryption and the LWE assumption. - We construct one-out-of-many unclonable predicate encryption (PE) from one-out-of-many indistinguishable-secure unclonable encryption and the LWE assumption. Thus, we obtain one-out-of-many indistinguishable-secure unclonable encryption, one-out-of-many copy-protection for single-bit output point functions, and one-out-of-many unclonable PE in the standard model from the LWE assumption. In addition, our one-time SDE scheme is the first SDE scheme that does not rely on any oracle heuristics and strong assumptions such as indistinguishability obfuscation and witness encryption.
Last updated:  2023-09-21
A note on ``ISG-SLAS: secure and lightweight authentication and key agreement scheme for industrial smart grid using fuzzy extractor''
Zhengjun Cao and Lihua Liu
We show that the key agreement scheme [J. Syst. Archit., 131:102698, 2022] fails to keep user anonymity and service provider anonymity, not as claimed. The scheme simply thinks that user anonymity is equivalent to protecting the target user's identity against exposure, while its long-term pseudo-identity can be exposed. We want to clarify that the true anonymity means that an adversary cannot attribute different sessions to different target users, even if the true identifier cannot be retrieved from the exposed pseudo-identifier.
Last updated:  2023-09-21
Publicly Verifiable Deletion from Minimal Assumptions
Fuyuki Kitagawa, Ryo Nishimaki, and Takashi Yamakawa
We present a general compiler to add the publicly verifiable deletion property for various cryptographic primitives including public key encryption, attribute-based encryption, and quantum fully homomorphic encryption. Our compiler only uses one-way functions, or more generally hard quantum planted problems for NP, which are implied by one-way functions. It relies on minimal assumptions and enables us to add the publicly verifiable deletion property with no additional assumption for the above primitives. Previously, such a compiler needs additional assumptions such as injective trapdoor one-way functions or pseudorandom group actions [Bartusek-Khurana-Poremba, CRYPTO 2023]. Technically, we upgrade an existing compiler for privately verifiable deletion [Bartusek-Khurana, CRYPTO 2023] to achieve publicly verifiable deletion by using digital signatures.
Last updated:  2023-09-21
Areion: Highly-Efficient Permutations and Its Applications (Extended Version)
Takanori Isobe, Ryoma Ito, Fukang Liu, Kazuhiko Minematsu, Motoki Nakahashi, Kosei Sakamoto, and Rentaro Shiba
In real-world applications, the overwhelming majority of cases require (authenticated) encryption or hashing with relatively short input, say up to 2K bytes. Almost all TCP/IP packets are 40 to 1.5K bytes, and the maximum packet lengths of major protocols, e.g., Zigbee, Bluetooth low energy, and Controller Area Network (CAN), are less than 128 bytes. However, existing schemes are not well optimized for short input. To bridge the gap between real-world needs (in the future) and limited performances of state-of-the-art hash functions and authenticated encryptions with associated data (AEADs) for short input, we design a family of wide-block permutations Areion that fully leverages the power of AES instructions, which are widely deployed in many devices. As for its applications, we propose several hash functions and AEADs. Areion significantly outperforms existing schemes for short input and even competitive to relatively long messages. Indeed, our hash function is surprisingly fast, and its performance is less than three cycles/byte in the latest Intel architecture for any message size. It is significantly much faster than existing state-of-the-art schemes for short messages up to around 100 bytes, which are the most widely-used input size in real-world applications, on both the latest CPU architectures (IceLake, Tiger Lake, and Alder Lake) and mobile platforms (Pixel 7, iPhone 14, and iPad Pro with Apple M2).
Last updated:  2023-09-21
Leveraging GPU in Homomorphic Encryption: Framework Design and Analysis of BFV Variants
Shiyu Shen, Hao Yang, Wangchen Dai, Lu Zhou, Zhe Liu, and Yunlei Zhao
Homomorphic Encryption (HE) enhances data security by facilitating computations on encrypted data, opening new paths for privacy-focused computations. The Brakerski-Fan-Vercauteren (BFV) scheme, a promising HE scheme, raises considerable performance challenges. Graphics Processing Units (GPUs), with considerable parallel processing abilities, have emerged as an effective solution. In this work, we present an in-depth study focusing on accelerating and comparing BFV variants on GPUs, including Bajard-Eynard-Hasan-Zucca (BEHZ), Halevi-Polyakov-Shoup (HPS), and other recent variants. We introduce a universal framework accommodating all variants, propose optimized BEHZ implementation, and first support HPS variants with large parameter sets on GPUs. Moreover, we devise several optimizations for both low-level arithmetic and high-level operations, including minimizing instructions for modular operations, enhancing hardware utilization for base conversion, implementing efficient reuse strategies, and introducing intra-arithmetic and inner-conversion fusion methods, thus decreasing the overall computational and memory consumption. Leveraging our framework, we offer comprehensive comparative analyses. Our performance evaluation showcases a marked speed improvement, achieving 31.9× over OpenFHE running on a multi-threaded CPU and 39.7% and 29.9% improvement, respectively, over the state-of-the-art GPU BEHZ implementation. Our implementation of the leveled HPS variant records up to 4× speedup over other variants, positioning it as a highly promising alternative for specific applications.
Last updated:  2023-09-21
XNET: A Real-Time Unified Secure Inference Framework Using Homomorphic Encryption
Hao Yang, Shiyu Shen, Siyang Jiang, Lu Zhou, Wangchen Dai, and Yunlei Zhao
Homomorphic Encryption (HE) presents a promising solution to securing neural networks for Machine Learning as a Service (MLaaS). Despite its potential, the real-time applicability of current HE-based solutions remains a challenge, and the diversity in network structures often results in inefficient implementations and maintenance. To address these issues, we introduce a unified and compact network structure for real-time inference in convolutional neural networks based on HE. We further propose several optimization strategies, including an innovative compression and encoding technique and rearrangement in the pixel encoding sequence, enabling a highly efficient batched computation and reducing the demand for time-consuming HE operations. To further expedite computation, we propose a GPU acceleration engine to leverage the massive thread-level parallelism to speed up computations. We test our framework with the MNIST, Fashion-MNIST, and CIFAR-10 datasets, demonstrating accuracies of 99.14%, 90.8%, and 61.09%, respectively. Furthermore, our framework maintains a steady processing speed of 0.46 seconds on a single-thread CPU, and a brisk 31.862 milliseconds on an A100 GPU for all datasets. This represents an enhancement in speed more than 3000 times compared to pervious work, paving the way for future explorations in the realm of secure and real-time machine learning applications.
Last updated:  2023-09-21
Efficient Hardware RNS Decomposition for Post-Quantum Signature Scheme FALCON
Samuel Coulon, Pengzhou He, Tianyou Bao, and Jiafeng Xie
The recently announced National Institute of Standards and Technology (NIST) Post-quantum cryptography (PQC) third-round standardization process has released its candidates to be standardized and Falcon is one of them. On the other hand, however, very few hardware implementation works for Falcon have been released due to its very complicated computation procedure and intensive complexity. With this background, in this paper, we propose an efficient hardware structure to implement residue numeral system (RNS) decomposition within NTRUSolve (a key arithmetic component for key generation of Falcon). In total, we have proposed three stages of coherent interdependent efforts to finish the proposed work. First, we have identified the necessary algorithmic operation related to RNS decomposition. Then, we have innovatively designed a hardware structure to realize these algorithms. Finally, field-programmable gate array (FPGA)-based implementation has been carried out to verify the superior performance of the proposed hardware structure. For instance, the proposed hardware design involves at least 3.91x faster operational time than the software implementation. To the authors' best knowledge, this is the first paper about the hardware acceleration of RNS decomposition for Falcon, and we hope the outcome of this work will facilitate the research in this area.
Last updated:  2023-09-20
Arithmetic Circuit Implementations of S-boxes for SKINNY and PHOTON in MPC
Aysajan Abidin, Erik Pohle, and Bart Preneel
Secure multi-party computation (MPC) enables multiple distrusting parties to compute a function while keeping their respective inputs private. In a threshold implementation of a symmetric primitive, e.g., of a block cipher, each party holds a share of the secret key or of the input block. The output block is computed without reconstructing the secret key. This enables the construction of distributed TPMs or transciphering for secure data transmission in/out of the MPC context. This paper investigates implementation approaches for the lightweight primitives SKINNY and PHOTON in arithmetic circuits. For these primitives, we identify arithmetic expressions for the S-box that result in smaller arithmetic circuits compared to the Boolean expressions from the literature. We validate the optimization using a generic actively secure MPC protocol and obtain 18% faster execution time with 49% less communication data for SKINNY-64-128 and 27% to 74% faster execution time with 49% to 81% less data for PHOTON $P_{100}$ and $P_{288}$. Furthermore, we find a new set of parameters for the heuristic method of polynomial decomposition, introduced by Coron, Roy and Vivek, specialized for SKINNY's 8-bit S-box. We reduce the multiplicative depth from 9 to 5.
Last updated:  2023-09-20
Noah's Ark: Efficient Threshold-FHE Using Noise Flooding
Morten Dahl, Daniel Demmler, Sarah El Kazdadi, Arthur Meyre, Jean-Baptiste Orfila, Dragos Rotaru, Nigel P. Smart, Samuel Tap, and Michael Walter
We outline a secure and efficient methodology to do threshold distributed decryption for LWE based Fully Homomorphic Encryption schemes. Due to the smaller parameters used in some FHE schemes, such as Torus-FHE (TFHE), the standard technique of ``noise flooding'' seems not to apply. We show that noise flooding can also be used with schemes with such small parameters, by utilizing a switch to a scheme with slightly higher parameters and then utilizing the efficient bootstrapping operations which TFHE offers. Our protocol is proved secure via a simulation argument, making its integration in bigger protocols easier to manage.
Last updated:  2023-09-20
Popping “R-propping”: breaking hardness assumptions for matrix groups over F_{2^8}
Fernando Virdia
A recent series of works (Hecht, IACR ePrint, 2020–2021) propose to build post-quantum public-key encapsulation, digital signatures, group key agreement and oblivious transfer from "R-propped" variants of the Symmetrical Decomposition and Discrete Logarithm problems for matrix groups over $\mathbb{F}_{2^8}$. We break all four proposals by presenting a linearisation attack on the Symmetrical Decomposition platform, a forgery attack on the signature scheme, and a demonstration of the insecurity of the instances of the Discrete Logarithm Problem used for signatures, group key agreement and oblivious transfer, showing that none of the schemes provides adequate security.
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.