Several Central Bank Digital Currency (CBDC) projects are considering the development of a digital currency that is managed on a permissioned blockchain, i.e. only authorized entities are involved in transactions verification. In this paper, we explore the best possible balance between privacy and accountability in such a traceable digital currency. Indeed, in case of suspicion of fraud or money laundering activity, it is important to enable the retrieval of the identity of a payer or a payee involved in a specific transaction. Based on a preliminary analysis of achievable anonymity properties in a transferable, divisible and traceable digital currency systems, we first present a digital currency framework along with the corresponding security and privacy model. Then, we propose a pairing-free traceable digital currency system that reconciles user's privacy protection and accountability. Our system is proven secure in the random oracle model.

Prime integers form the basis for finite field and elliptic curve cryptography, as well as many other applications. Provable prime generation guarantees primality and is more efficient than probabilistic generation, and provides components for an efficient primality proof. This paper details a protocol which takes in the proof components from the generation process, proves primality, and as an added benefit, supplies the user with a subgroup generator.

A verifiable timed signature (VTS) scheme allows one to time-lock a signature on a known message for a given amount of time $T$ such that after performing a sequential computation for time $T$ anyone can extract the signature from the time-lock. Verifiability ensures that anyone can publicly check if a time-lock contains a valid signature on the message without solving it first, and that the signature can be obtained by solving the same for time $T$. This work formalizes VTS, presents efficient constructions compatible with BLS, Schnorr, and ECDSA signatures, and experimentally demonstrates that these constructions can be employed in practice. On a technical level, we design an efficient cut-and-choose protocol based on the homomorphic time-lock puzzles to prove the validity of a signature encapsulated in a time-lock puzzle. We also present a new efficient {range proof} protocol that significantly improves upon existing proposals in terms of the proof size, and is also of independent interest. While VTS is a versatile tool with numerous existing applications, we demonstrate VTS's applicability to resolve three novel challenging issues in the space of cryptocurrencies. Specifically, we show how VTS is the cryptographic cornerstone to construct: (i) Payment channel networks with improved on-chain unlinkability of users involved in a transaction, (ii) multi-party signing of transactions for cryptocurrencies without any on-chain notion of time and (iii) cryptocurrency-enabled fair multi-party computation protocol.

In this paper, we completely study two classes of Boolean functions that are suited for hybrid symmetric-FHE encryption with stream ciphers like FiLIP. These functions (which we call homomorphic-friendly) need to satisfy contradictory constraints: 1) allow a fast homomorphic evaluation, and have then necessarily a very elementary structure, 2) be secure, that is, allow the cipher to resist all classical attacks (and even more, since guess and determine attacks are facilitated in such framework). Because of constraint 2, these functions need to have a large number of variables (often more than 1000), and this makes even more difficult to satisfy constraint 1 (hence the interest of these two classes). We determine exactly all the main cryptographic parameters (algebraic degree, resiliency order, nonlinearity, algebraic immunity) for all functions in these two classes and we give close bounds for the others (fast algebraic immunity, dimension of the space of annihilators of minimal degree). This is the first time that this is done for all functions in classes of a sufficient cryptographic interest.

Private stream aggregation (PSA) allows an untrusted data aggregator to compute statistics over a set of multiple participants' data while ensuring the data remains private. Existing works rely on a trusted third party to enable an aggregator to achieve fault tolerance, that requires interactive recovery, but in the real world this may not be practical or secure. We develop a new formal framework for PSA that accounts for user faults, and can support non-interactive recovery, while still supporting strong individual privacy guarantees. We first must define a new level of security in the presence of faults and malicious adversaries because the existing definitions do not account for faults and the security implications of the recovery. After this we develop the first protocol that provably reaches this level of security, i.e., individual inputs are private even after the aggregator's recovery, and reach new levels of scalability and communication efficiency over existing work seeking to support fault tolerance. The techniques we develop are general, and can be used to augment any PSA scheme to support non-interactive fault recovery.

CPU caches are a powerful source of information leakage. To develop practical cache-based attacks, there is an increasingly need to automate the process of finding exploitable cache-based side-channels in computer systems. Cache template attack is a generic technique that utilizes Flush+Reload attack in order to automatically exploit cache vulnerability of Intel platforms. Cache template attack on T-table-based AES implementation consists of two phases including the profiling phase and the key exploitation phase. Profiling is a preprocessing phase to monitor dependencies between the secret key and behavior of the cache memory. In addition, the addresses of T-tables can be obtained automatically. In the key exploitation phase, most significant bits (MSBs) of the secret key bytes are retrieved by monitoring exploitable addresses. In this paper, we propose a simple yet effective searching technique which accelerates the profiling phase by a factor of at most 64. To verify the theoretical model of our technique, we implement the described attack on AES. The experimental results showed the profiling phase runtime of the cache template attack is around 10 minutes while our method speeds up the running of this phase to around 9 seconds.

With the NIST Post quantum cryptography competition in final round, the importance of implementation security is highlighted in the latest call. In this regard, we report practical side-channel assisted message recovery attacks over embedded implementations of several post-quantum public key encryption (PKE) and key encapsulation mechanisms (KEM) based on the Learning With Errors (LWE) and Learning With Rounding (LWR) problem, which include three finalists and three semi-finalist candidates of the NIST standardization process. The proposed attacks target storage of the decrypted message in memory, a basic operation found in all libraries and typically unavoidable in any embedded implementation. We also identify interesting ciphertext malleability properties for LWE/LWR-based PKEs and exploit them to generalise proposed attack to different implementation choices as well as implementations protected with side-channel countermeasures such as shuffling and masking. All proposed attacks are validated on ARM Cortex-M4 microcontroller, targeting optimized open source implementations of PQC schemes using electromagnetic side-channel measurements.

This article explores the use of elliptic curves with order 2r = 2 mod 4, which we call double-odd elliptic curves. This is a very large class, comprising about 1/4th of all curves over a given field. On such curves, we manage to define a prime order group with appropriate characteristics for building cryptographic protocols: - Element encoding is canonical, and verified upon decoding. For a 2n-bit group (with n-bit security), encoding size is 2n + 1 bits, i.e. as good as compressed points on classic prime order curves. - Unified and complete formulas allow secure and efficient computations in the group. - Efficiency is on par with twisted Edwards curves, and in some respects slightly better; e.g. half of double-odd curves have formulas for computing point doublings with only six multiplications (down to 1M+5S per doubling on some curves). We describe here various formulas and discuss implementations. We also define two specific parameter choices for curves with 128-bit security, called do255e and do255s. Our own implementations on 64-bit x86 (Coffee Lake) and low-end ARM Cortex M0+ achieve generic point multiplication in 76696 and 2.19 million cycles, respectively, with curve do255e.

Our main result is a quantum public-key encryption scheme based on the Extrapolated Di- hedral Coset problem (EDCP) which is equivalent, under quantum polynomial-time reductions, to the Learning With Errors (LWE) problem. For limited number of public keys (roughly linear in the security parameter), the proposed scheme is information-theoretically secure. For poly- nomial number of public keys, breaking the scheme is as hard as solving the LWE problem. The public keys in our scheme are quantum states of size Õ(n) qubits. The key generation and decryption algorithms require Õ(n) qubit operations while the encryption algorithm takes O(1) qubit operations.

In this work we focus on improving the communication complexity of the \emph{online phase} of honest majority MPC protocols. To this end, we present a general and simple method to compile arbitrary secret-sharing-based passively secure protocols defined over an arbitrary ring that are secure up to additive attacks in a malicious setting, to actively secure protocols with abort. The resulting protocol has a total communication complexity in the online phase of $1.5(n-1)$ shares, which amounts to $1.5$ shares per party asymptotically. An important aspect of our techniques is that they can be seen as generalization of ideas that have been used in other works in a rather \emph{ad-hoc} manner for different secret-sharing protocols. Thus, our work serves as a way of unifying key ideas in recent honest majority protocols, to understand better the core techniques and similarities among these works. Furthermore, for $n=3$, when instantiated with replicated secret-sharing-based protocols (Araki et al.~CCS 2016), the communication complexity in the online phase amounts to only $1$ ring element per party, matching the communication complexity of the BLAZE protocol (Patra \& Suresh, NDSS 2020), while having a much simpler design.

LWE based key-exchange protocols lie at the heart of post-quantum public-key cryptography. However, all existing protocols either lack the non-interactive nature of Diffie-Hellman key-exchange or polynomial LWE-modulus, resulting in unwanted efficiency overhead. We study the possibility of designing non-interactive LWE-based protocols with polynomial LWE-modulus. To this end, • We identify and formalize simple non-interactive and polynomial LWE-modulus variants of existing protocols, where Alice and Bob simultaneously exchange one or more (ring) LWE samples with polynomial LWE-modulus and then run individual key reconciliation functions to obtain the shared key. • We point out central barriers and show that such non-interactive key-exchange protocols are impossible if: 1) the reconciliation functions first compute the inner product of the received LWE sample with their private LWE secret. This impossibility is information theoretic. 2) one of the reconciliation functions does not depend on the error of the transmitted LWE sample. This impossibility assumes hardness of LWE. • We give further evidence that progress in either direction, of giving an LWE-based NIKE protocol or proving impossibility of one will lead to progress on some other well-studied questions in cryptography. Overall, our results show possibilities and challenges in designing simple (ring) LWE-based non-interactive key exchange protocols.

Physical security of NIST lightweight cryptography competition candidates is gaining importance as the standardization process progresses. Side-channel attacks (SCA) are a well-researched topic within the physical security of cryptographic implementations. It was shown that collisions in the intermediate values can be captured by side-channel measurements to reduce the complexity of the key retrieval to trivial numbers. In this paper, we target a specific bit permutation vulnerability in the block cipher GIFT that allows the attacker to mount a key recovery attack. We present a novel SCA methodology called DCSCA - Differential Ciphertext SCA, which follows principles of differential fault analysis, but instead of the usage of faults, it utilizes SCA and statistical distribution of intermediate values. We simulate the attack on a publicly available bitslice implementation of GIFT, showing the practicality of the attack. We further show the application of the attack on GIFT-based AEAD schemes (GIFT-COFB, ESTATE, HYENA, and SUNDAE-GIFT) proposed for the NIST LWC competition. DCSCA can recover the master key with $2^{13.39}$ AEAD sessions, assuming 32 encryptions per session.

Nowadays, information is known as the main asset of each organization, which causes data generation to be exponentially increasing. Hence, different capacity issues and requirements show up with it, e.g. storage and maintenance of generating data, searching among them, and analyzing them. Cloud computing is one of the common technologies used to meet these requirements. Popularity of this technology is extremely growing as it can be used to handle high amount of data in a cost efficient and highly available (anytime and anywhere) manner. However, there are still extensive security challenges (e.g. data confidentiality) with this technology. Cryptography is one of the main methods used to fulfill privacy preserving of people and organizations. Encryption methods can impressively keep data private, so it is not possible to search among encrypted messages in order to retrieve information, after applying traditional encryption. Searchable encryption can enable searching among encrypted data and overcome this shortage. However, much more research is required to enable whole data searching while proper level of security would be achieved for these systems. In this paper, a technique to perform searching by the third party is introduced. When a number of nodes are interacting and some of them may upload malicious documents, this technique can be useful. Furthermore, document categorization is another application of the referred scheme.

Password-hardened encryption (PHE) was introduced by Lai et al. at USENIX 2018 and immediately productized by VirgilSecurity. PHE is a password-based key derivation protocol that involves an oblivious external crypto service for key derivation. The security of PHE protects against offline brute-force attacks, even when the attacker is given the entire database. Furthermore, the crypto service neither learns the derived key nor the password. PHE supports key-rotation meaning that both the server and crypto service can update their keys without involving the user. While PHE significantly strengthens data security, it introduces a single point of failure because key-derivation always requires access to the crypto service. In this work, we address this issue and simultaneously increase security by introducing threshold password-hardened encryption. Our formalization of this primitive revealed shortcomings of the original PHE definition that we also address in this work. Following the spirit of prior works, we give a simple and efficient construction using lightweight tools only. We also implement our construction and evaluate its efficiency. Our experiments confirm the practical efficiency of our scheme and show that it is more efficient than common memory-hard functions, such as scrypt. From a practical perspective this means that threshold PHE can be used as an alternative to scrypt for password protection and key-derivation, offering better security in terms of offline brute force attacks.

Oblivious RAM enables oblivious access to memory in the single-client setting, which may not be the best fit in the network setting. Multi-client oblivious RAM (MCORAM) considers a collaborative but untrusted environment, where a database owner selectively grants read access and write access to different entries of a confidential database to multiple clients. Their access pattern must remain oblivious not only to the server but also to fellow clients. This upgrade rules out many techniques for constructing ORAM, forcing us to pursue new techniques. MCORAM not only provides an alternative solution to private anonymous data access (Eurocrypt 2019) but also serves as a promising building block for equipping oblivious file systems with access control and extending other advanced cryptosystems to the multi-client setting. Despite being a powerful object, the current state-of-the-art is unsatisfactory: The only existing scheme requires $O(\sqrt n)$ communication and client computation for a database of size $n$. Whether it is possible to reduce these complexities to $\mathsf{polylog}(n)$, thereby matching the upper bounds for ORAM, is an open problem, i.e., can we enjoy access control and client-obliviousness under the same bounds? Our first result answers the above question affirmatively by giving a construction from fully homomorphic encryption (FHE). Our main technical innovation is a new technique for cross-key trial evaluation of ciphertexts. We also consider the same question in the setting with $N$ non-colluding servers, out of which at most $t$ of them can be corrupt. We build multi-server MCORAM from distributed point functions (DPF), and propose new constructions of DPF via a virtualization technique with bootstrapping, assuming the existence of homomorphic secret sharing and pseudorandom generators in NC0, which are not known to imply FHE.

A ring signature scheme allows the signer to sign on behalf of an ad hoc set of users, called a ring. The verifier can be convinced that a ring member signs, but cannot point to the exact signer. Ring signatures have become increasingly important today with their deployment in anonymous cryptocurrencies. Conventionally, it is implicitly assumed that all ring members are equally likely to be the signer. This assumption is generally false in reality, leading to various practical and devastating deanonymizing attacks in Monero, one of the largest anonymous cryptocurrencies. These attacks highlight the unsatisfactory situation that how a ring should be chosen is poorly understood. We propose an analytical model of ring samplers towards a deeper understanding of them through systematic studies. Our model helps to describe how anonymous a ring sampler is with respect to a given signer distribution as an information-theoretic measure. We show that this measure is robust, in the sense that it only varies slightly when the signer distribution varies slightly. We then analyze three natural samplers -- uniform, mimicking, and partitioning -- under our model with respect to a family of signer distributions modeled after empirical Bitcoin data. We hope that our work paves the way towards researching ring samplers from a theoretical point of view.

The Cheon-Kim-Kim-Song (CKKS) scheme (Asiacrypt'17) is one of the most promising homomorphic encryption (HE) schemes as it enables privacy-preserving computing over real (or complex) numbers. It is known that bootstrapping is the most challenging part of the CKKS scheme. Further, homomorphic evaluation of modular reduction is the core of the CKKS bootstrapping, but as modular reduction is not represented by the addition and multiplication of complex numbers, approximate polynomials for modular reduction should be used. The best-known techniques (Eurocrypt'21) use a polynomial approximation for trigonometric functions and their composition. However, all the previous methods are based on an indirect approximation, and thus it requires lots of multiplicative depth to achieve high accuracy. This paper proposes a direct polynomial approximation of modular reduction for CKKS bootstrapping, which is optimal in error variance and depth. Further, we propose an efficient algorithm, namely the lazy baby-step giant-step (BSGS) algorithm, to homomorphically evaluate the approximate polynomial, utilizing the lazy relinearization/rescaling technique. The lazy-BSGS reduces the computational complexity by half compared to the ordinary BSGS algorithm. The performance improvement for the CKKS scheme by the proposed algorithm is verified by implementation over HE libraries. The implementation results show that the proposed method has a multiplicative depth of 10 for modular reduction to achieve state-of-the-art accuracy, while the previous methods have depths of 11 to 12. Moreover, we achieve higher accuracies within a small multiplicative depth, for example, 93-bit within multiplicative depth 11.

Public-key encryption (PKE) schemes or key-encapsulation mechanisms (KEMs) are fundamental cryptographic building blocks to realize secure communication protocols. There are several known transformations that generically turn weakly secure schemes into strongly (i.e., IND-CCA) secure ones. While most of these transformations require the weakly secure scheme to provide perfect correctness, Hofheinz, Hövelmanns, and Kiltz (HHK) (TCC 2017) have recently shown that variants of the Fujisaki-Okamoto (FO) transform can work with schemes that have negligible correctness error in the (quantum) random oracle model (QROM). Many recent schemes in the NIST post-quantum competition (PQC) use variants of these transformations. Some of their CPA-secure versions even have a non-negligible correctness error and so the techniques of HHK cannot be applied. In this work, we study the setting of generically transforming PKE schemes with potentially large, i.e., non-negligible, correctness error to ones having negligible correctness error. While there have been previous treatments in an asymptotic setting by Dwork, Naor, and Reingold (EUROCRYPT 2004), our goal is to come up with practically efficient compilers in a concrete setting and apply them in two different contexts. Firstly, we show how to generically transform weakly secure deterministic or randomized PKEs into CCA-secure KEMs in the (Q)ROM using variants of HHK. This applies to essentially all candidates to the NIST PQC based on lattices and codes with non-negligible error for which we provide an extensive analysis. We thereby show that it improves some of the code-based candidates. Secondly, we study puncturable KEMs in terms of the Bloom Filter KEM (BFKEM) proposed by Derler et al. (EUROCRYPT 2018) which inherently have a non-negligible correctness error. BFKEMs are a building block to construct fully forward-secret zero round-trip time (0-RTT) key-exchange protocols. In particular, we show the first approach towards post-quantum secure BFKEMs generically from lattices and codes by applying our techniques to identity-based encryption (IBE) schemes with (non-)negligible correctness error.

Distributed ORAM (DORAM) is a multi-server variant of Oblivious RAM. Originally proposed to lower bandwidth, DORAM has recently been of great interest due to its applicability to secure computation in the RAM model, where circuit complexity and rounds of communication are equally important metrics of efficiency. In this work, we construct the first DORAM schemes in the 2-server, semi-honest setting that simultaneously achieve sublinear server computation and constant rounds of communication. We provide two constant-round constructions, one based on square root ORAM that has $O(\sqrt{N}\log N)$ local computation and another based on secure computation of a doubly efficient PIR that achieves local computation of $O(N^\epsilon)$ for any $\epsilon > 0$ but that allows the servers to distinguish between reads and writes. As a building block in the latter construction, we provide secure computation protocols for evaluation and interpolation of multivariate polynomials based on the Fast Fourier Transform, which may be of independent interest.

The latest pandemic COVID-19 brought governments worldwide to use various containment measures to control its spread, such as contact tracing, social distance regulations, and curfews. Epidemiological simulations are commonly used to assess the impact of those policies before they are implemented. Unfortunately, the scarcity of relevant empirical data, specifically detailed social contact graphs, hampered their predictive accuracy. As this data is inherently privacy-critical, a method is urgently needed to perform powerful epidemiological simulations on real-world contact graphs without disclosing any sensitive information. In this work, we present RIPPLE, a privacy-preserving epidemiological modeling framework enabling standard models for infectious disease on a population’s real contact graph while keeping all contact information locally on the participants’ devices. As a building block of independent interest, we present PIR-SUM, a novel extension to private information retrieval for secure download of element sums from a database. Our protocols are supported by a proof-of-concept implementation, demonstrating a 2-week simulation over half a million participants completed in 7 minutes, with each participant communicating less than 50 KB.

In this article, we discuss basic strategies that can be used to implement block ciphers in both software and hardware environments. As models for discussion, we use substitution-permutation networks which form the basis for many practical block cipher structures. For software implementation, we discuss approaches such as table lookups and bit-slicing, while for hardware implementation, we examine a broad range of architectures from high speed structures like pipelining, to compact structures based on serialization. To illustrate different implementation concepts, we present example data associated with specific methods and discuss sample designs that can be employed to realize different implementation strategies. We expect that the article will be of particular interest to researchers, scientists, and engineers that are new to the field of cryptographic implementation.

A single-sign-on (SSO) is an authentication system that allows a user to log in with a single identity and password to any of several related, yet independent, server applications. SSO solutions eliminate the need for users to repeatedly prove their identities to different applications and hold different credentials for each application. Token-based authentication is commonly used to enable an SSO experience on the web, and on enterprise networks. A large body of work considers distributed token generation which can protect the long-term keys against a subset of breached servers. A recent work (CCS'18) introduced the notion of Password-based Threshold Authentication (PbTA) with the goal of making password-based token generation for SSO secure against server breaches that could compromise both long-term keys and user credentials. They also introduced a generic framework called PASTA that can instantiate a PbTA system. The existing SSO systems built on distributed token generation techniques, including the PASTA framework, do not admit password-update functionality. In this work, we address this issue by proposing a password-update functionality into the PASTA framework. We call the modified framework PAS-TA-U. As a concrete application, we instantiate PAS-TA-U to implement in Python a distributed SSH key manager for enterprise networks (ESKM) that also admits a password-update functionality for its clients. Our experiments show that the overhead of protecting secrets and credentials against breaches in our system compared to a traditional single server setup is low (average 119 ms in a 10-out-of-10 server setting on Internet with 80 ms round trip latency).

Contact tracing is an important mitigation tool for national health services to fight epidemics such as COVID-19. While many of the existing approaches for automated contact tracing focus on privacy-preserving decentralized solutions, the use of blockchain in these applications is often suggested for the transparency and immutability of the data being collected. We present CovidBloc, a contact tracing system that implements the COVID 19 exposure database on Hyperledger Fabric Blockchain Network. Like most decentralized contact tracing application, the participants of the CovidBloc are: (1) a mobile application running on a bluetooth-equipped smartphone, (2) a web dashboard for health officials, and (3) a backend server acting as a repository for data being collected. We have implemented all components of CovidBloc to make it a fully functional contact tracing application. It is hosted at https://anonymous.4open.science/r/c6caad6d-62a4-463c-8301-472e421b931f/. The mobile application for CovidBloc is developed for Android. The exposure notification system in our mobile application is implemented as per the recently released draft documentation by Google and Apple. The exposure notification API from Google and Apple is only available to a limited number of teams per country. The backend server is an important component of any automated contact tracing system which acts as a repository for exposure data to be pushed by smartphones upon authorization by the health staff. Since adding or removing information on the server has privacy consequences, it is required that the server should not be trusted. The backend server for CovidBloc is implemented on Hyperledger Fabric Blockchain network.

In the current world of the Internet-of-things and edge computing, computations are increasingly performed locally on small connected systems. As such, those devices are often vulnerable to adversarial physical access, enabling a plethora of physical attacks which is a challenge even if such devices are built for security. As cryptography is one of the cornerstones of secure communication among devices, the pertinence of fault attacks is becoming increasingly apparent in a setting where a device can be easily accessed in a physical manner. In particular, two recently proposed fault attacks, Statistical Ineffective Fault Attack (SIFA) and the Fault Template Attack (FTA) are shown to be formidable due to their capability to bypass the common duplication based countermeasures. Duplication based countermeasures, deployed to counter the Differential Fault Attack (DFA), work by duplicating the execution of the cipher followed by a comparison to sense the presence of any effective fault, followed by an appropriate recovery procedure. While a handful of countermeasures are proposed against SIFA, no such countermeasure is known to thwart FTA to date. In this work, we propose a novel countermeasure based on duplication, which can protect against both SIFA and FTA. The proposal is also lightweight with only a marginally additional cost over simple duplication based countermeasures. Our countermeasure further protects against all known variants of DFA, including Selmke, Heyszl, Sigl’s attack from FDTC 2016. It does not inherently leak side-channel information and is easily adaptable for any symmetric key primitive. The validation of our countermeasure has been done through gate-level fault simulation.

Private Set Intersection (PSI) allows two parties to obtain the intersection of their data sets while revealing nothing else. PSI is attractive in many scenarios and has wide applications in academia and industry. Over the last three decades, a large number of PSI protocols have been proposed using different cryptographic techniques, under different assumptions, for different scenarios. The inherent complexity, heterogeneous constructions, and rapid evolution of PSI protocols make it difficult to have a unified perspective and further promote the field. We make the following three contributions to present a pragmatic benchmark of two-party PSI. First, we propose the Map-and-Compare framework, which generalizes almost all efficient PSI constructions to date, and intuitively explains the idea and challenge of PSI constructions. Based on the framework, we divide existing proposals into several categories and perform a systematic analysis of the features and use cases of different PSI variants. Second, we present a Java-based benchmark library that implements almost all two-party PSI protocols (which are considered to define the state-of-the-art in terms of concrete performance) and supports rapid prototyping of new PSI protocols. Third, by using our library as a common ground, we provide a comprehensive and impartial comparison of all our PSI implementations in detail. We discuss the performance of different proposals in various settings.

Lattice-based algorithms in cryptanalysis often search for a target vector satisfying integer linear constraints as a shortest or closest vector in some lattice. In this work, we observe that these formulations may discard non-linear information from the underlying application that can be used to distinguish the target vector even when it is far from being uniquely close or short. We formalize lattice problems augmented with a predicate distinguishing a target vector and give algorithms for solving instances of these problems. We apply our techniques to lattice-based approaches for solving the Hidden Number Problem, a popular technique for recovering secret DSA or ECDSA keys in side-channel attacks, and demonstrate that our algorithms succeed in recovering the signing key for instances that were previously believed to be unsolvable using lattice approaches. We carried out extensive experiments using our estimation and solving framework, which we also make available with this work.

We discuss the setting of information-theoretically secure channel protocols where confidentiality of transmitted data should hold against unbounded adversaries. We argue that there are two possible scenarios: One is that the adversary is currently bounded, but stores today's communication and tries to break confidentiality later when obtaining more computational power or time. We call channel protocols protecting against such attacks future-secure. The other scenario is that the adversary already has extremely strong computational powers and may try to use that power to break current executions. We call channels withstanding such stronger attacks unconditionally-secure. We discuss how to instantiate both future-secure and unconditionally-secure channels. To this end we first establish according confidentiality and integrity notions, then prove the well-known composition theorem to also hold in the information-theoretic setting: Chosen-plaintext security of the channel protocol, together with ciphertext integrity, implies the stronger chosen-ciphertext notion. We discuss how to build future-secure channel protocols by combining computational message authentication schemes like HMAC with one-time pad encryption. Chosen-ciphertext security follows easily from the generalized composition theorem. We also show that using one-time pad encryption with the unconditionally-secure Carter-Wegman MACs we obtain an unconditionally-secure channel protocol.

Semi-regular sequences over $\mathbb{F}_2$ are sequences of homogeneous elements of the algebra $ B^{(n)}=\mathbb{F}_2[X_1,...,X_n]/(X_1^2,...,X_n^2)$, which have as few relations between them as possible. It is believed that most such systems are semi-regular and this property has important consequences for understanding the complexity of Grobner basis algorithms such as F4 and F5 for solving such systems. In fact even in one of the simplest and most important cases, that of quadratic sequences of length $n$ in $n$ variables, the question of the existence of semi-regular sequences for all $n$ remains open. In this paper we present a new framework for the concept of semiregularity which we hope will allow the use of ideas and machinery from homological algebra to be applied to this interesting and important open question. First we introduce an analog of the Koszul complex and show that $\mathbb{F}_2$-semi-regularity can be characterized by the exactness of this complex. We show how the well known formula for the Hilbert series of a semiregular sequence can be deduced from the Koszul complex. Finally we show that the concept of first fall degree also has a natural description in terms of the Koszul complex.

Aggregate signcryption combines the functionalities of aggregate signature and encryption. Very recently, Zia & Ali [1] (Wireless Personal Communications, https://doi.org/10.1007/s11277-020-07637-z) proposed an elliptic curve cryptography (ECC) based multi-recipient aggregate signcryption scheme. The authors claimed that their scheme is correct, efficient, and secure against known attacks. However, by this comment, we show that their scheme is incorrect and the receiver(s) is unable to unsigncrypt the message.

Polynomial commitment schemes (PCS) have recently been in the spotlight for their key role in building SNARKs. A PCS provides the ability to commit to a polynomial over a finite field and prove its evaluation at points. A succinct PCS has commitment and evaluation proof size sublinear in the degree of the polynomial. An efficient PCS has sublinear proof verification. Any efficient and succinct PCS can be used to construct a SNARK with similar security and efficiency characteristics (in the random oracle model). Proof-carrying data (PCD) enables a set of parties to carry out an indefinitely long distributed computation where every step along the way is accompanied by a proof of correctness. It generalizes incrementally verifiable computation and can even be used to construct SNARKs. Until recently, however, the only known method for constructing PCD required expensive SNARK recursion. A system called Halo first demonstrated a new methodology for building PCD without SNARKs, exploiting an aggregation property of the Bulletproofs inner-product argument. The construction was heuristic because it makes non-black-box use of a concrete instantiation of the Fiat-Shamir transform. We expand upon this methodology to show that PCD can be (heuristically) built from any homomorphic polynomial commitment scheme (PCS), even if the PCS evaluation proofs are neither succinct nor efficient. In fact, the Halo methodology extends to any PCS that has an even more general property, namely the ability to aggregate linear combinations of commitments into a new succinct commitment that can later be opened to this linear combination. Our results thus imply new constructions of SNARKs and PCD that were not previously described in the literature and serve as a blueprint for future constructions as well.

Prime integers are the backbone of most public key cryptosystems. Attacks often go after the primes themselves, as in the case of all factoring and index calculus algorithms. Primes are time sensitive cryptographic material and should be periodically changed. Unfortunately many systems use fixed primes for a variety of reasons, including the difficulty of generating trusted, random, cryptographically secure primes. This is particularly concerning in the case of discrete log based cryptosystems. This paper describes a variant of provable prime generation, intended for discrete logarithm based cryptography, based off Pocklington's theorem with improved efficiency, flexibility and security.

Recently, as the number of IoT (Internet of Things) devices has increased, the use of lightweight cryptographic algorithms that are suitable for environments with scarce resources has also increased. Consequently, the safety of such cryptographic algorithms is becoming increasingly important. Among them, side-channel analysis methods are very realistic threats. In this paper, we propose a novel differential fault attack method on the Lightweight Encryption Algorithm (LEA) cipher which became the ISO/IEC international standard lightweight cryptographic algorithm in 2019. Previously proposed differential fault attack methods on the LEA used the Single Bit Flip model, making it difficult to apply to real devices. The proposed attack method uses a more realistic attacker assumption, the Random Word Error model. We demonstrate that the proposed attack method can be implemented on real devices using an electromagnetic fault injection setup. Our attack method has the weakest attacker assumption among attack methods proposed to date. In addition, the number of required fault-injected ciphertexts and the number of key candidates for which exhaustive search is performed are the least among all existing methods. Therefore, when implementing the LEA cipher on IoT deivces, designers must apply appropriate countermeasures against fault injection attacks.

We present passive attacks against CKKS, the homomorphic encryption scheme for arithmetic on approximate numbers presented at Asiacrypt 2017. The attack is both theoretically efficient (running in expected polynomial time) and very practical, leading to complete key recovery with high probability and very modest running times. We implemented and tested the attack against major open source homomorphic encryption libraries, including HEAAN, SEAL, HElib and PALISADE, and when computing several functions that often arise in applications of the CKKS scheme to machine learning on encrypted data, like mean and variance computations, and approximation of logistic and exponential functions using their Maclaurin series. The attack shows that the traditional formulation of IND-CPA security (or indistinguishability against chosen plaintext attacks) achieved by CKKS does not adequately capture security against passive adversaries when applied to approximate encryption schemes, and that a different, stronger definition is required to evaluate the security of such schemes. We provide a solid theoretical basis for the security evaluation of homomorphic encryption on approximate numbers (against passive attacks) by proposing new definitions, that naturally extend the traditional notion of INDCPA security to the approximate computation setting. We propose both indistinguishability-based and simulation-based variants, as well as restricted versions of the definitions that limit the order and number of adversarial queries (as may be enforced by some applications). We prove implications and separations among different definitional variants, and discuss possible modifications to CKKS that may serve as a countermeasure to our attacks.

An oblivious PRF, or OPRF, is a protocol between a client and a server, where the server has a key $k$ for a secure pseudorandom function $F$, and the client has an input $x$ for the function. At the end of the protocol the client learns $F(k,x)$, and nothing else, and the server learns nothing. An OPRF is verifiable if the client is convinced that the server has evaluated the PRF correctly with respect to a prior commitment to $k$. OPRFs and verifiable OPRFs have numerous applications, such as private-set-intersection protocols, password-based key-exchange protocols, and defense against denial-of-service attacks. Existing OPRF constructions use RSA-, Diffie-Hellman-, and lattice-type assumptions. The first two are not post-quantum secure. In this paper we construct OPRFs and verifiable OPRFs from isogenies. Our main construction uses isogenies of supersingular elliptic curves over $\mathbb{F}_{p^{2}}$ and tries to adapt the Diffie-Hellman OPRF to that setting. However, a recent attack on supersingular-isogeny systems due to Galbraith et al. [ASIACRYPT 2016] makes this approach difficult to secure. To overcome this attack, and to validate the server's response, we develop two new zero-knowledge protocols that convince each party that its peer has sent valid messages. With these protocols in place, we obtain an OPRF in the SIDH setting and prove its security in the UC framework. Our second construction is an adaptation of the Naor-Reingold PRF to commutative group actions. Combining it with recent constructions of oblivious transfer from isogenies, we obtain an OPRF in the CSIDH setting.

Access and search pattern leakage from range queries are detrimental to the security of encrypted databases, as evidenced by a large body of work on efficient attacks that reconstruct one-dimensional databases. Recently, the first attack from 2D range queries showed that higher-dimensional databases are also in danger. This attack requires complete information for reconstruction. In this paper, we develop reconstructions that require less information. We present an order reconstruction attack that only depends on access pattern leakage, and empirically show that the order allows the attacker to infer the geometry of the underlying data. Notably, this attack also achieves full database reconstruction when the 1D horizontal and vertical projections of the points are dense. We also give an approximate database reconstruction attack that is distribution-agnostic and works with any subset of the possible search pattern, given the order of the database. Finally, we show how knowledge of auxiliary information such as the centroid of a related dataset allows to improve the reconstruction. We support our results with formal analysis and experiments on real-world databases and queries drawn from various distributions.

Cloud computing and cloud storage are among the most efficient technologies for storing and processing metadata. But there are many privacy concerns within this domain. Most of the challenges are coming from trusted or semi trusted cloud servers where some computations must be applied to high confidential data. Data encryption can solve some confidentiality issues on the cloud but it is not easy to provide privacy preserving data processing services such as searching a query over encrypted data. On the other hand implementing searchable encryption algorithms in cloud infrastructure helps providing data confidentiality and privacy preserving data processing and can provide searching capability as well, which is the most important step of selecting a document. First in this article, some injection attacks against searchable public key encryption schemes are described. To be more specific message injection attack and index injection attack are applied against PEKS and PERKS schemes. Afterwards, two new schemes are proposed that are secure against them and are based of dPEKS and SAE-I. Finally, efficiency and security of proposed schemes are analyzed, and some implementation issues were discussed.

We revisit and take a closer look at a (not so well known) result of a 2017 paper, showing that the differential uniformity of any vectorial function is bounded from below by an expression depending on the size of its image set. We make explicit the resulting tight lower bound on the image set size of differentially $\delta$-uniform functions. We also significantly improve an upper bound on the nonlinearity of vectorial functions obtained in the same reference and involving their image set size. We study when the resulting bound is sharper than the covering radius bound. We obtain as a by-product a lower bound on the Hamming distance between differentially $\delta$-uniform functions and affine functions, which we improve significantly with a second bound. This leads us to study what can be the maximum Hamming distance between vectorial functions and affine functions. We provide an upper bound which is slightly sharper than a bound by Liu, Mesnager and Chen when $m< n$, and a second upper bound, which is much stronger in the case (happening in practice) where $m$ is near $n$; we study the tightness of this latter bound; this leads to an interesting question on APN functions, to which we answer. We finally make more precise the bound on the differential uniformity which was the starting point of the paper.

We study the notion of zero-knowledge secure against quantum polynomial-time verifiers (referred to as quantum zero-knowledge) in the concurrent composition setting. Despite being extensively studied in the classical setting, concurrent composition in the quantum setting has hardly been studied. We initiate a formal study of concurrent quantum zero-knowledge. Our results are as follows: - Bounded Concurrent QZK for NP and QMA: Assuming post-quantum one-way functions, there exists a quantum zero-knowledge proof system for NP in the bounded concurrent setting. In this setting, we fix a priori the number of verifiers that can simultaneously interact with the prover. Under the same assumption, we also show that there exists a quantum zero-knowledge proof system for QMA in the bounded concurrency setting. - Quantum Proofs of Knowledge: Assuming quantum hardness of learning with errors (QLWE), there exists a bounded concurrent zero-knowledge proof system for NP satisfying quantum proof of knowledge property. Our extraction mechanism simultaneously allows for extraction probability to be negligibly close to acceptance probability (extractability) and also ensures that the prover's state after extraction is statistically close to the prover's state after interacting with the verifier (simulatability). The seminal work of [Unruh EUROCRYPT'12], and all its followups, satisfied a weaker version of extractability property and moreover, did not achieve simulatability. Our result yields a proof of quantum knowledge system for QMA with better parameters than prior works.

Interactive oracle proofs (IOPs) are a multi-round generalization of probabilistically checkable proofs that play a fundamental role in the construction of efficient cryptographic proofs. We present an IOP that simultaneously achieves the properties of zero knowledge, linear-time proving, and polylogarithmic-time verification. We construct a zero-knowledge IOP where, for the satisfiability of an $N$-gate arithmetic circuit over any field of size $\Omega(N)$, the prover uses $O(N)$ field operations and the verifier uses $\polylog(N)$ field operations (with proof length $O(N)$ and query complexity $\polylog(N)$). Polylogarithmic verification is achieved in the holographic setting for every circuit (the verifier has oracle access to a linear-time-computable encoding of the circuit whose satisfiability is being proved). Our result implies progress on a basic goal in the area of efficient zero knowledge. Via a known transformation, we obtain a zero knowledge argument system where the prover runs in linear time and the verifier runs in polylogarithmic time; the construction is plausibly post-quantum and only makes a black-box use of lightweight cryptography (collision-resistant hash functions).

We consider the problem of verifiable and private delegation of computation [Gennaro et al. CRYPTO'10] in which a client stores private data on an untrusted server and asks the server to compute functions over this data. In this scenario we aim to achieve three main properties: the server should not learn information on inputs and outputs of the computation (privacy), the server cannot return wrong results without being caught (integrity), and the client can verify the correctness of the outputs faster than running the computation (efficiency). A known paradigm to solve this problem is to use a (non-private) verifiable computation (VC) to prove correctness of a homomorphic encryption (HE) evaluation on the ciphertexts. Despite the research advances in obtaining efficient VC and HE, using these two primitives together in this paradigm is concretely expensive. Recent work [Fiore et al. CCS'14, PKC'20] addressed this problem by designing specialized VC solutions that however require the HE scheme to work with very specific parameters; notably HE ciphertexts must be over $\mathbb{Z}_q$ for a large prime $q$. In this work we propose a new solution that allows a flexible choice of HE parameters, while staying modular (based on the paradigm combining VC and HE) and efficient (the VC and the HE schemes are both executed at their best efficiency). At the core of our new protocol are new homomorphic hash functions for Galois rings. As an additional contribution we extend our results to support non-deterministic computations on encrypted data and an additional privacy property by which verifiers do not learn information on the inputs of the computation.

Modern digital signature schemes can provide more guarantees than the standard notion of (strong) unforgeability, such as offering security even in the presence of maliciously generated keys, or requiring to know a message to produce a signature for it. The use of signature schemes that lack these properties has previously enabled attacks on real-world protocols. In this work we revisit several of these notions beyond unforgeability, establish relations among them, provide the first formal definition of non re-signability, and two generic transformations that can provide these properties for a given signature scheme in a provable and efficient way. Our results are not only relevant for established schemes: for example, the ongoing NIST PQC competition towards standardizing post-quantum signature schemes had six candidates in its third round of which three are to be standardized. We perform an in-depth analysis of all the candidates with respect to their security properties beyond unforgeability. We show that many of them do not yet offer these stronger guarantees, which implies that the security guarantees of these post-quantum schemes are not strictly stronger than, but instead incomparable to, classical signature schemes. We show how applying our transformations would efficiently solve this, paving the way for the standardized schemes to provide these additional guarantees and thereby making them harder to misuse.

ForkAE is a NIST lightweight cryptography candidate that uses the forkcipher primitive in two modes of operation -- SAEF and PAEF -- optimized for authenticated encryption of the shortest messages. SAEF is a sequential and online AEAD that minimizes the memory footprint compared to its alternative parallel mode PAEF, catering to the most constrained devices. SAEF was proven AE secure against nonce-respecting adversaries. Due to their more acute and direct exposure to device misuse and mishandling, in most use cases of lightweight cryptography, nonce reuse presents a very realistic attack vector. Furthermore, many lightweight applications mandate security for their online AEAD schemes against block-wise adversaries. Surprisingly, very few NIST lightweight AEAD candidates come with provable guarantees against these security threats. In this work, we investigate the provable security guarantees of SAEF when nonces are repeated under a refined version of the notion of online authenticated encryption OAE given by Fleischmann et al. in 2012. We apply Using the coefficient H technique we show that, with no modifications, SAEF is OAE secure up to the birthday security bound, i.e., up to $2^{n/2}$ processed blocks of data, where $n$ is the block size of the forkcipher. The implications of our work are that SAEF is safe to use in a block-wise fashion, and that if nonces get repeated, this has no impact on ciphertext integrity and confidentiality only degrades by a limited extent up to repetitions of common message prefixes.

Double-block Hash-then-Sum (DbHtS) MACs are a class of MACs that aim for achieving beyond-birthday-bound security, including SUM-ECBC, PMAC\_Plus, 3kf9 and LightMAC_Plus. Recently Datta et al. (FSE'19), and then Kim et al. (Eurocrypt'20) prove that DbHtS constructions are secure beyond the birthday bound in the single-user setting. However, by a generic reduction, their results degrade to (or even worse than) the birthday bound in the multi-user setting. In this work, we revisit the security of DbHtS MACs in the multi-user setting. We propose a generic framework to prove beyond-birthday-bound security for DbHtS constructions. We demonstrate the usability of this framework with applications to key-reduced variants of DbHtS MACs, including 2k-SUM-ECBC, 2k-PMAC_Plus and 2k-LightMAC_Plus. Our results show that the security of these constructions will not degrade as the number of users grows. On the other hand, our results also indicate that these constructions are secure beyond the birthday bound in both single-user and multi-user setting without additional domain separation, which is used in the prior work to simplify the analysis. Moreover, we find a critical flaw in 2kf9, which is proved to be secure beyond the birthday bound by Datta et al. (FSE'19). We can successfully forge a tag with probability 1 without making any queries. We go further to show attacks with birthday-bound complexity on several variants of 2kf9.

Ledger systems are applications run on peer-to-peer networks that provide strong integrity guarantees. However, these systems often have high participation costs. For a server to join this network, the bandwidth and computation costs grow linearly with the number of state transitions processed; for a client to interact with a ledger system, it must either maintain the entire ledger system state like a server or trust a server to correctly provide such information. In practice, these substantial costs centralize trust in the hands of the relatively few parties with the resources to maintain the entire ledger system state. The notion of *incrementally verifiable computation*, introduced by Valiant (TCC '08), has the potential to significantly reduce such participation costs. While prior works have studied incremental verification for basic payment systems, the study of incremental verification for a general class of ledger systems remains in its infancy. In this paper we initiate a systematic study of incremental verification for ledger systems, including its foundations, implementation, and empirical evaluation. We formulate a cryptographic primitive providing the functionality and security for this setting, and then demonstrate how it captures applications with privacy and user-defined computations. We build a system that enables incremental verification, for applications such as privacy-preserving payments, with universal (application-independent) setup. Finally, we show that incremental verification can reduce participation costs by orders of magnitude, for a bare-bones version of Bitcoin.

We present a modification to RingCT protocol with stealth addresses that makes it compatible with Delegated Proof of Stake based consensus mechanisms called Delegated RingCT. Our scheme has two building blocks: a customised version of an Integrated Signature and Encryption scheme composed of a public key encryption scheme and two signature schemes (a digital signature and a linkable ring signature); and non-interactive zero knowledge proofs. We give a description of the scheme, security proofs and a prototype implementation whose benchmarking is discussed. Although Delegated RingCT does not have the same degree of anonymity as other RingCT constructions, we argue that the benefits that the compatibility with DPoS consensus mechanisms brings constitute a reasonable trade-off for being able to develop an anonymous decentralised cryptocurrency faster and more scalable than existing ones.

Recent independent analyses by Bonnetain-Schrottenloher and Peikert in Eurocrypt 2020 significantly reduced the estimated quantum security of the isogeny-based commutative group action key-exchange protocol CSIDH. This paper refines the estimates of a resource-constrained quantum collimation sieve attack to give a precise quantum security to CSIDH. Furthermore, we optimize large CSIDH parameters for performance while still achieving the NIST security levels 1, 2, and 3. Finally, we provide a C-code constant-time implementation of those CSIDH large instantiations using the square-root-complexity Vélu’s formulas recently proposed by Bernstein, De Feo, Leroux and Smith.

In this paper, we present a strong, formal, and general-purpose cryptographic model for privacy-preserving authenticated key exchange (PPAKE) protocols. PPAKE protocols are secure in the traditional AKE sense but additionally guarantee the confidentiality of the identities used in communication sessions. Our model has several useful and novel features, among others: it is a proper extension of classical AKE models, guarantees in a strong sense that the confidentiality of session keys is independent from the secrecy of the used identities, and it is the first to support what we call dynamic modes, where the responsibility of selecting the identities of the communication partners may vary over several protocol runs. To the best of our knowlegde, this implements the first technical approach to deal with protocol options in AKE security models. We show the validity of our model by applying it to the cryptographic core of IPsec IKEv2 with signature-based authentication where the need for dynamic modes is practically well-motivated. In our analysis, we not only show that this protocol provides strong classical AKE security guarantees but also that the identities that are used by the parties remain hidden in successful protocol runs. Historically, the Internet Key Exchange (IKE) protocol was the first real-world AKE to incorporate privacy-preserving techniques. However, lately privacy-preserving techniques have gained renewed interest in the design process of important protocols like TLS 1.3 (with encrypted SNI) and NOISE. We believe that our new model can be a solid foundation to analyze these and other practical protocols with respect to their privacy guarantees, in particular, in the now so wide-spread scenario where multiple virtual servers are hosted on a single machine.

Recent studies and incidents have shed light on the threat posed by botnets consisting of a large set of relatively weak IoT devices that host an army of bots. However, little is known about the threat posed by a small set of devices that are not infected with malware and do not host bots. In this paper, we present Botnet-IND (indirect), a new type of distributed attack which is launched by a botnet consisting of botless IoT devices. In order to demonstrate the feasibility of Botnet-IND on commercial, off-the-shelf IoT devices, we present Piping Botnet, an implementation of Botnet-IND on smart irrigation systems, a relatively new type of IoT device which is used by both the private and public sector to save water; such systems will likely replace all traditional irrigation systems in the next few years. We perform a security analysis of three of the five most sold commercial smart irrigation systems (GreenIQ, BlueSpray, and RainMachine). Our experiments demonstrate how attackers can trick such irrigation systems (Wi-Fi and cellular) without the need to compromise them with malware or bots. We show that in contrast to traditional botnets that require a large set of infected IoT devices to cause great harm, Piping Botnet can pose a severe threat to urban water services using a relatively small set of smart irrigation systems. We found that only 1,300 systems were required to drain a floodwater reservoir when they are maliciously prog

Innovative side-channel attacks have repeatedly falsified the assumption that cryptographic implementations are opaque black-boxes. Therefore, it is essential to ensure cryptographic constructions' security even when information leaks via unforeseen avenues. One such fundamental cryptographic primitive is the secret-sharing schemes, which underlies nearly all threshold cryptography. Our understanding of the leakage-resilience of secret-sharing schemes is still in its preliminary stage. This work studies locally leakage-resilient linear secret-sharing schemes. An adversary can leak $m$ bits of arbitrary local leakage from each $n$ secret shares. However, in a locally leakage-resilient secret-sharing scheme, the leakage's joint distribution reveals no additional information about the secret. For every constant $m$, we prove that the Massey secret-sharing scheme corresponding to a random linear code of dimension $k$ (over sufficiently large prime fields) is locally leakage-resilient, where $k/n > 1/2$ is a constant. The previous best construction by Benhamouda, Degwekar, Ishai, Rabin (CRYPTO--2018) needed $k/n > 0.907$. A technical challenge arises because the number of all possible $m$-bit local leakage functions is exponentially larger than the number of random linear codes. Our technical innovation begins with identifying an appropriate pseudorandomness-inspired family of tests; passing them suffices to ensure leakage-resilience. We show that most linear codes pass all tests in this family. This Monte-Carlo construction of linear secret-sharing scheme that is locally leakage-resilient has applications to leakage-resilient secure computation. Furthermore, we highlight a crucial bottleneck for all the analytical approaches in this line of work. Benhamouda et al. introduced an analytical proxy to study the leakage-resilience of secret-sharing schemes; if the proxy is small, then the scheme is leakage-resilient. However, we present a one-bit local leakage function demonstrating that the converse is false, motivating the need for new analytically well-behaved functions that capture leakage-resilience more accurately. Technically, the analysis involves probabilistic and combinatorial techniques and (discrete) Fourier analysis. The family of new ``tests'' capturing local leakage functions, we believe, is of independent and broader interest.

In this short note, we explain how to reduce the time to compute all $N$ proofs in the Pointproofs vector commitment (VC) scheme by Gorbunov et al., from $O(N^2)$ time to $O(N\log{N})$. The key ingredient is representing the computation of all proofs as a product between a Toeplitz matrix and the committed vector, which can be computed fast using Discrete Fourier Transforms (DFTs). We quickly prototype our algorithm in C++ and show it is much faster than the naive algorithm for computing all proofs in Pointproofs.

Almost perfect nonlinear functions possess the optimal resistance to the differential cryptanalysis and are widely studied. Most known APN functions are obtained as functions over finite fields $GF(2^n)$ and very little is known about combinatorial constructions of them in $\mathbb{F}_2^n$. In this work we propose two approaches for obtaining quadratic APN functions in $\mathbb{F}_2^n$. The first approach exploits a secondary construction idea, it considers how to obtain a quadratic APN function in $n+1$ variables from a given quadratic APN function in $n$ variables using special restrictions on new terms. The second approach is searching quadratic APN functions that have matrix form partially filled with standard basis vectors in a cyclic manner. This approach allowed us to find a new APN function in 7 variables. We proved that the updated list of quadratic APN functions in dimension 7 is complete up to CCZ-equivalence.

The fixed-Hessian minimisation method can be used to implement privacy-preserving machine learning training from homomorphic encryption. This is a relatively under-explored part of the literature, with the main prior work being that of Bonte and Vercauteren (BMC Medical Genomics, 2018), who proposed a simplified Hessian method for logistic regression training over the BFV homomorphic encryption scheme. Our main contribution is to revisit the fixed- Hessian approach for logistic regression training over the CKKS homomorphic encryption scheme. We improve on the prior work in several aspects, most notably showing how the native encoding in CKKS can be used to take advantage of SIMD operations. We implement our new fixed-Hessian approach in SEAL and compare it to more commonly-used minimisation methods, based on Gradient Descent and Nesterov’s Accelerated Gradient Descent. We find that the fixed-Hessian approach exhibits fast run time and comparable accuracy to these alternative approaches. Moreover, it can be argued to be more practical in the privacy-preserving training context, as no step size parameter needs to be chosen. As an additional contribution, we describe and implement three distinct training algorithms, based on Gradient Descent, Nesterov’s Accelerated Gradient Descent, and a fixed-Hessian method respec- tively, to achieve privacy-preserving ridge regression training from homomorphic encryption. To the best of our knowledge, this is the first time homomorphic encryption has been used to implement ridge regression training on encrypted data.

Bernstein et al. recently introduced a system ``Elligator'' for steganographic key distribution. At the heart of their construction are invertible maps between a finite field $\mathbb{F}$ and an elliptic curve $\mathcal{E}$ over $\mathbb{F}$. There are two such maps, called $\phi$ in the ``Elligator 1'' system, and $\psi$ in the ``Elligator 2'' system. Here we show two ways to construct hash functions from $\psi$ which are indifferentiable from a random oracle. Because $\psi$ is relatively simple, our analyses are also simple. One of our constructions uses a novel ``wallpapering'' approach, whereas the other uses the hash-twice-and-add approach of Brier et al.

Benchmarking the performance of companies is essential to identify improvement potentials in various industries. Due to a competitive environment, this process imposes strong privacy needs, as leaked business secrets can have devastating effects on participating companies. Consequently, related work proposes to protect sensitive input data of companies using secure multi-party computation or homomorphic encryption. However, related work so far does not consider that also the benchmarking algorithm, used in today's applied real-world scenarios to compute all relevant statistics, itself contains significant intellectual property, and thus needs to be protected. Addressing this issue, we present PCB — a practical design for Privacy-preserving Company Benchmarking that utilizes homomorphic encryption and a privacy proxy — which is specifically tailored for realistic real-world applications in which we protect companies' sensitive input data and the valuable algorithms used to compute underlying key performance indicators. We evaluate PCB's performance using synthetic measurements and showcase its applicability alongside an actual company benchmarking performed in the domain of injection molding, covering 48 distinct key performance indicators calculated out of hundreds of different input values. By protecting the privacy of all participants, we enable them to fully profit from the benefits of company benchmarking.

The lack of privacy in the first generation of cryptocurrencies such as Bitcoin, Ethereum, etc. is a well known problem in cryptocurrency research. To overcome this problem, several new cryptocurrencies were designed to guarantee transaction privacy and anonymity for their users (examples include ZCash, Monero, etc.). However, the anonymity provided by such systems appears to be fundamentally problematic in current business and legislation settings: banks and other financial institutions must follow rules such as "Know your customer" (KYC), "Anti Money Laundering" (AML), etc. It is also well known that the (alleged or real) anonymity guarantees provided by cryptocurrencies have attracted ill-intentioned individual to this space, who look at cryptocurrencies as a way of facilitating illegal activities (tax-evasion, ransom-ware, trading of illegal substances, etc.). The fact that current cryptocurrencies do not comply with such regulations can in part explain why traditional financial institutions have so far been very sceptical of the ongoing cryptocurrency and Blockchain revolution. In this paper, we propose a novel design principle for identity management in Blockchains. The goal of our design is to maintain privacy, while still allowing compliance with current regulations and preventing exploitations of Blockchain technology for purposes which are incompatible with the social good.

A quantum bit commitment scheme is to realize bit (rather than qubit) commitment by exploiting quantum communication and quantum computation. In this work, we study the binding property of the quantum string commitment scheme obtained by composing a generic quantum perfectly(resp. statistically)-hiding computationally-binding bit commitment scheme (which can be realized based on quantum-secure one-way permutations(resp. functions)) in parallel. We show that the resulting scheme satisfies a stronger quantum computational binding property, which we will call predicate-binding, than the trivial honest-binding. Intuitively and very roughly, the predicate-binding property guarantees that given any inconsistent predicate pair over a set of strings (i.e. no strings in this set can satisfy both predicates), if a (claimed) quantum commitment can be opened so that the revealed string satisfies one predicate with certainty, then the same commitment cannot be opened so that the revealed string satisfies the other predicate (except for a negligible probability). As an application, we plug a generic quantum perfectly(resp. statistically)-hiding computationally-binding bit commitment scheme in Blum's zero-knowledge protocol for the NP-complete language Hamiltonian Cycle. The quantum computational soundness of the resulting protocol will follow immediately from the quantum computational predicate-binding property of commitments. Combined with the perfect(resp. statistical) zero-knowledge property which can be similarly established as in previous work, this gives rise to the first quantum perfect(resp. statistical) zero-knowledge argument system (with soundness error 1/2) for all NP languages based solely on quantum-secure one-way permutations(resp. functions).

The typical login protocol for authenticating a user to a web service involves the client sending a password over a TLS-secured channel to the service, occasionally deployed with the password being prehashed. This widely-deployed paradigm, while simple in nature, is prone to both inadvertent logging and eavesdropping attacks, and has repeatedly led to the exposure of passwords in plaintext. Partly to address this problem, symmetric and asymmetric PAKE protocols were developed to ensure that the messages exchanged during an authentication protocol reveal nothing about the passwords. However, these protocols inherently require at least two messages to be sent out: one from each party. This limitation hinders wider adoption, as the most common login flow consists of a single message from client to the login server. The ideal solution would retain the password privacy properties of asymmetric PAKEs while allowing the protocol to be a drop-in replacement into legacy password-over-TLS deployments. With these requirements in mind, we introduce the notion of credential-hiding login, which enables a client to authenticate itself by sending a single message to the server, while ensuring the correct verification of credentials and maintaining credential privacy in the same strong sense as guaranteed by asymmetric PAKEs. We initiate a formal study of this primitive in the Universal Composability framework, design and implement a practical password-based protocol using identity-based encryption, and report on its performance. We also construct a variant of credential-hiding login for fuzzy secrets (e.g. biometrics), proven secure based on the Learning With Errors (LWE) assumption.

Quantum pseudorandom functions (QPRFs) extend the classical security of a PRF by allowing the adversary to issue queries on input superposition. Zhandry [Zhandry, FOCS 2012] showed a separation between the two notions and proved that common construction paradigms are also quantum secure, albeit with a new ad-hoc analysis. In this work, we revisit the question of constructing QPRFs and propose a new method starting from small-domain (classical) PRFs: At the heart of our approach is a new domain-extension technique based on bipartite expanders. Interestingly, our analysis is almost entirely classical. As a corollary of our main theorem, we obtain the first (approximate) key homomorphic quantum PRF based on the quantum intractability of the learning with errors problem.

RSA key generation requires devices to generate large prime numbers. The naïve approach is to generate candidates at random, and then test each one for (probable) primality. However, it is faster to use a sieve method, where the candidates are chosen so as not to be divisible by a list of small prime numbers $\{p_i\}$. Sieve methods can be somewhat complex and time-consuming, at least by the standards of embedded and hardware implementations, and they can be tricky to defend against side-channel analysis. Here we describe an improvement on Joye et al.'s sieve based on the Chinese Remainder Theorem (CRT). We also describe a new sieve method using quadratic residuosity which is simpler and faster than previously known methods, and which can produce values in desired RSA parameter ranges such as $(2^{n-1/2}, 2^n)$ with minimal additional work. The same methods can be used to generate strong primes and DSA moduli. We also demonstrate a technique for RSA private key operations using the Chinese Remainder Theorem (RSA-CRT) without $q^{-1}$ mod $p$. This technique also leads to inversion-free batch RSA and inversion-free RSA mod $p^k q$. We demonstrate how an embedded device can use our key generation and RSA-CRT techniques to perform RSA efficiently without storing the private key itself: only a symmetric seed and one or two short hints are required.

Side-channel attacks targeting cryptography may leak only partial or indirect information about the secret keys. There are a variety of techniques in the literature for recovering secret keys from partial information. In this tutorial, we survey several of the main families of partial key recovery algorithms for RSA, (EC)DSA, and (elliptic curve) Diffie-Hellman, the public-key cryptosystems in common use today. We categorize the known techniques by the structure of the information that is learned by the attacker, and give simplified examples for each technique to illustrate the underlying ideas.

In this paper we construct and consider a signature scheme with evolving secret key, where there is used Type 3 pairing. The idea is based on some properties of binary trees, with a number of leaves being the same as a number of time periods in the scheme. This lets us to gain such conditions, that allows to prove the forward-security of the considered scheme in the random oracle model. The proof is conducted by reducing the security of the scheme to the difficulty of solving a certain counterpart of the Weak $\ell$-th Bilinear Diffie-Hellman Inversion problem. In addition to that, we construct an interactive signature scheme with evolving private key and justify that it is forward-secure blind scheme.

Seven years ago, a famous case in which data from a Fitbit tracker was used in the courtroom in a personal injury case heralded a new age: the age of testifying wearable devices. Prior to that, data from wearable devices was used in various areas, including medicine, advertising, and scientific research, but the use of such data in the Fitbit case attracted the interest of a new sector: the legal sector. Since then, lawyers, investigators, detectives, and police officers have used data from pacemakers and smartwatches in order to prove/disprove allegations regarding wearable device owners in several well-known cases (sexual assault, arson, personal injury, etc.). In this paper, we discuss testifying wearable devices. We explain the advantages of wearable devices over traditional IoT devices in the legal setting, the parties involved in cases in which a wearable device was used to testify against/for the device owner, and the information flow. We then focus on an interesting area of research: intoxication detection. We explain the motivation to detect whether a subject was intoxicated and explain the primary scientific gap in this area. In order to overcome this gap, we suggest a new method for detecting whether a subject was intoxicated based on free gait data obtained from a wearable device. We evaluate the performance of the proposed method in a user study involving 30 subjects and show that motion sensor data obtained from a smartphone and fitness tracker from eight seconds of free gait can indicate whether a subject is/was intoxicated (obtaining an AUC of 0.97) and thus be used as testimony. Finally, we analyze the current state and the near future of the age of testifying wearable devices and explain why we believe that (1) we are still at the beginning of this age despite the fact that seven years has passed since the original court case, and (2) the number of cases in which wearable device data is used to testify for/against the device owner is expected to increase significantly in the next few years.

Quantum computing capability outperforms that of the classic computers overwhelmingly, which seriously threatens modern public-key cryptography. For this reason, the National Institute of Standards and Technology (NIST) and several other standards organizations are progressing the standardization for post-quantum cryptography (PQC). There are two contenders among those candidates, CRYSTALS-KYBER and SABER, lattice-based encryption algorithms in the third round finalists of NIST's PQC standardization project. At the current phase, it is important to evaluate their security, which is based on the hardness of the variants of Ring Learning With Errors (Ring-LWE) problem. In ProvSec 2020, Wang et al. introduced a notion of "meta-PKE" for Ring-LWE crypto mechanism. They further proposed randomness reuse attacks on NewHope and LAC cryptosystems which meet the meta-PKE model. In their attacks, the encryptor Bob's partial (or even all) randomness can be recovered if it is reused. In this paper, we propose attacks against CRYSTALS-KYBER and SABER crypto schemes by adapting the meta-PKE model and improving Wang et al.'s methods. Then, we show that our proposed attacks cost at most 4, 3, and 4 queries to recover Bob's randomness for any security levels of I (AES-128), III (AES-192), and V (AES-256), respectively in CRYSTALS-KYBER. Simultaneously, no more than 6, 6, and 4 queries are required to recover Bob's secret for security levels I, III, and V in SABER.

In a witness encryption scheme, to decrypt a ciphertext associated with an NP statement, the decrypter takes as input a witness testifying that the statement is in the language. When the statement is not in the language, then the message is hidden. Thus far, the only provably secure constructions assume the existence of indistinguishability obfuscation (iO) and multilinear maps (MMaps). We make progress towards building polynomially efficient witness encryption for NP without resorting to iO or MMaps. In particular, we give a witness encryption scheme from Yao's garbled circuit technique and a new type of fully homomorphic encryption (FHE) that we call annihilating. Interestingly, we require a version of the annihilating FHE that is circularly insecure, i.e., allows testing the presence of a key cycle. We prove our witness encryption's security from a novel assumption about our annihilating FHE. We formulate the assumption as an interplay between an annihilating FHE and ideal ciphers. We show a candidate (leveled) annihilating FHE built from a multikey variant of the BGV/BFV fully homomorphic cryptosystems.

We present PANCAKE, the first system to protect key-value stores from access pattern leakage attacks with small constant factor bandwidth overhead. PANCAKE uses a new approach, that we call frequency smoothing, to transform plaintext accesses into uniformly distributed encrypted accesses to an encrypted data store. We show that frequency smoothing prevents access pattern leakage attacks by passive persistent adversaries in a new formal security model. We integrate PANCAKE into three key-value stores used in production clusters, and demonstrate its practicality: on standard benchmarks, PANCAKE achieves 229× better throughput than non-recursive Path ORAM - within 3–6× of insecure baselines for these key-value stores.

MiniQCrypt is a world where quantum-secure one-way functions exist, and quantum communication is possible. We construct an oblivious transfer (OT) protocol in MiniQCrypt that achieves simulation-security in the plain model against malicious quantum polynomial-time adversaries, building on the foundational work of Bennett, Brassard, Crépeau and Skubiszewska (CRYPTO 1991). Combining the OT protocol with prior works, we obtain secure two-party and multi-party computation protocols also in MiniQCrypt. This is in contrast to the classical world, where it is widely believed that one-way functions alone do not give us OT. In the common random string model, we achieve a constant-round universally composable (UC) OT protocol.

The Hybrid Public Key Encryption (HPKE) scheme is an emerging standard currently under consideration by the Crypto Forum Research Group (CFRG) of the IETF as a candidate for formal approval. Of the four modes of HPKE, we analyse the authenticated mode HPKE_Auth in its single-shot encryption form as it contains what is, arguably, the most novel part of HPKE and has applications to other upcoming standards such as MLS. HPKE_Auth’s intended application domain is captured by a new primitive which we call Authenticated Public Key Encryption (APKE). We provide syntax and security definitions for APKE schemes, as well as for the related Authenticated Key Encapsulation Mechanisms (AKEMs). We prove security of the AKEM scheme DH-AKEM underlying HPKE_Auth based on the Gap Diffie-Hellman assumption and provide general AKEM/DEM composition theorems with which to argue about HPKE_Auth’s security. To this end, we also formally analyse HPKE_Auth’s key schedule and key derivation functions. To increase confidence in our results we use the automatic theorem proving tool CryptoVerif. All our bounds are quantitative and we discuss their practical implications for HPKE_Auth. As an independent contribution we propose the new framework of nominal groups that allows us to capture abstract syntactical and security properties of practical elliptic curves, including the Curve25519 and Curve448 based groups (which do not constitute cyclic groups).

EPID systems are anonymous authentication protocols where a device can be revoked by including one of its signatures in a revocation list. Such protocols are today included in the ISO/IEC 20008-2 standard and are embedded in billions of chips, which make them a flagship of advanced cryptographic tools. Yet, their security analysis is based on a model that suffers from several important limitations, which either questions the security assurances EPID can provide in the real world or prevents such systems from achieving their full impact. The most prominent example is the one of revocation lists. Although they could be managed locally by verifiers, which would be natural in most use-cases, the security model assumes that they are managed by a trusted entity, a requirement that is not easily met in practice and that is thus tempting to ignore, as illustrated in the corresponding standard. In this paper, we propose to revisit the security model of EPID, by removing some limitations of previous works but mostly by answering the following question: what can we achieve when revocation lists are generated by a malicious entity? Surprisingly, even in this disadvantageous context, we show that it is possible to retain strong properties that we believe to better capture the spirit of EPID systems. Moreover, we show that we can construct very efficient schemes resisting such powerful adversaries by essentially tweaking previous approaches. In particular, our constructions do not require to perform any significant test on the revocation lists during the signature generation process. These constructions constitute the second contribution of this paper.

Optimization of finite field arithmetic is important for the deployment of public key cryptography, particularly in the context of elliptic curve cryptography. Until now the primary concern has been operations over the prime field $\F_p$, where $p$ is a prime. With the advent of pairing-based cryptography there arises a need to also look at optimal arithmetic over extension fields $\F_{p^n}$ for small values of $n$. Here we focus on the determination of quadratic residuosity and the calculation of inverses and square roots over these fields, operations often carried out in conjunction with one another. We demonstrate with a minor improvement in a hash-to-curve algorithm, and a major speed-up in the calculation of square roots in quadratic extensions.

In this paper, we study the connections between pseudo-free families of computational $\Omega$-algebras (in appropriate varieties of $\Omega$-algebras for suitable finite sets $\Omega$ of finitary operation symbols) and certain standard cryptographic primitives. We restrict ourselves to families $(H_d\,|\,d\in D)$ of computational $\Omega$-algebras (where $D\subseteq\{0,1\}^*$) such that for every $d\in D$, each element of $H_d$ is represented by a unique bit string of length polynomial in the length of $d$. Very loosely speaking, our main results are as follows: (i) pseudo-free families of computational mono-unary algebras with one-to-one fundamental operation (in the variety of all mono-unary algebras) exist if and only if one-way families of permutations exist; (ii) for any $m\ge2$, pseudo-free families of computational $m$-unary algebras with one-to-one fundamental operations (in the variety of all $m$-unary algebras) exist if and only if claw-resistant families of $m$-tuples of permutations exist; (iii) for a certain $\Omega$ and a certain variety $\mathfrak V$ of $\Omega$-algebras, the existence of pseudo-free families of computational $\Omega$-algebras in $\mathfrak V$ implies the existence of families of trapdoor permutations.

An important security risk in cloud Field-Programmable Gate Arrays (FPGAs) is power wasting, occurring when a design exercises excessive switching activity with the intention to cause voltage-drop related faults in the host FPGA or, in the extreme case, FPGA reset and denial-of-service. In this paper, we introduce the idea of infiltrating undercover sensors for monitoring the fluctuations of FPGA core voltage. Our approach ensures that the shell has full control over sensor placement, done so that FPGA users do not have to sacrifice an inch of their design space nor to be aware that the voltage-fluctuations caused by their design are being monitored. Additionally, we describe how to design voltage-drop sensors that have higher coverage than the state-of-the-art alternatives and experimentally demonstrate that our sensors are indeed able to accurately monitor voltage fluctuations across the entire FPGA. Finally, we propose a novel metric which, after applied on sensor measurements, reveals the location of the source of the highest activity on the FPGA.

With every new generation, high-end FPGAs are becoming richer in features and resources, making the usage model of single-user per FPGA decreasingly cost-efficient. Although virtualized FPGAs enable multiple users to share the same FPGA, this multi-tenancy is not employed in practice because of potential security threats, such as voltage attacks. These attacks use power-wasting circuits to exercise excessive switching activity on the target FPGA to cause extreme voltage fluctuations, which produce timing faults in collocated circuits or, in extreme cases, reset target FPGA. In this work, we present the idea of automated embedding of the on-chip voltage sensors into the virtualized FPGAs and continuous monitoring of the core voltage for suspected fluctuations caused by a voltage attacker. Our sensors are nonintrusive and placement-adaptive because we implement them immediately after placing and routing the user design with resources that are left unused. We devise a novel measurement technique to continuously analyze the sensor outputs and locate the power-wasting circuits. Additionally, we are the first to use a synchronous power-wasting attacker, capable of producing timing faults, on Xilinx 7-series FPGAs and to successfully locate it. Hence, our proposed monitoring system enables the virtualized FPGA to identify the voltage attackers, at minimal cost, and prevent them from repeating the attack.

This paper presents detailed and computer-verified proofs of formulas that, given a permutation pi of 2^m indices with m>=1, produce control bits for a standard permutation network that uses 2^m(m-1/2) swaps to apply pi to a list. The formulas match the control bits computed by a serial algorithm of Stone (1968) and a parallel algorithm of Nassimi–Sahni (1982). The proofs are a step towards computer-verified correctness proofs for efficient implementations of these algorithms.

We examine some historical proto-mechanical cryptographic devices, such as the Wheatstone Cryptograph, that employ revolving clock hands or rotating concentric disks. The action of these “cipher clocks” can be factored into a stream cipher followed by a monoalphabetic substitution. This allows us to perform a stochastic hill-climbing attack to break the substitution. The attack maximizes a fitness that measures how well a decryption of the substitution cipher resembles an encryption of the stream cipher alone.

In this paper we introduce partitioning oracles, a new class of decryption error oracles which, conceptually, take a ciphertext as input and output whether the decryption key belongs to some known subset of keys. We introduce the first partitioning oracles which arise when encryption schemes are not committing with respect to their keys. We detail novel adaptive chosen ciphertext attacks that exploit partitioning oracles to efficiently recover passwords and de-anonymize anonymous communications. The attacks utilize efficient key multi-collision algorithms --- a cryptanalytic goal that we define --- against widely used authenticated encryption with associated data (AEAD) schemes, including AES-GCM, XSalsa20/Poly1305, and ChaCha20/Poly1305. We build a practical partitioning oracle attack that quickly recovers passwords from Shadowsocks proxy servers. We also survey early implementations of the OPAQUE protocol for password-based key exchange, and show how many could be vulnerable to partitioning oracle attacks due to incorrectly using non-committing AEAD. Our results suggest that the community should standardize and make widely available committing AEAD to avoid such vulnerabilities.

Sanitizable signatures (SaS) allow a (single) sanitizer, chosen by the signer, to modify and re-sign a message in a somewhat controlled way, that is, only editing parts (or blocks) of the message that are admissible for modification. This primitive is an efficient tool, with many formally defined security properties, such as unlinkability, transparency, immutability, invisibility, and unforgeability. An SaS scheme that satisfies these properties can be a great asset to the privacy of any field it will be applied to, e.g., anonymizing medical files. In this work, we look at the notion of &#947;-sanitizable signatures ( &#947;SaS): we take the sanitizable signatures one step further by allowing the signer to not only decide which blocks can be modified, but also how many of them at most can be modified within a single sanitization, setting a limit, denoted with &#947;. We adapt the security properties listed above to &#947;SaS and propose our own scheme, ULISS (Unlinkable Limited Invisible Sanitizable Signature), then show that it verifies these properties. This extension of SaS can not only improve current use cases, but also introduce new ones, e.g., restricting the number of changes in a document within a certain timeframe.

In universally composable (UC) security, a global setup is intended to capture the ideal behavior of a primitive which is accessible by multiple protocols, allowing them to share state. A representative example is the Bitcoin ledger. Indeed, since Bitcoin---and more generally blockchain ledgers---are known to be useful in various scenarios, it has become increasingly popular to capture such ledgers as global setup. Intuitively, one would expect UC to allow us to make security statements about protocols that use such a global setup, e.g., a global ledger, which can then be automatically translated into the setting where the setup is replaced by a protocol implementing it, such as Bitcoin. We show that the above reasoning is flawed and such a generic security-preserving replacement can only work under very (often unrealistic) strong conditions on the global setup and the security statement. For example, the UC security of Bitcoin for realizing a ledger proved by Badertscher et al. [CRYPTO'17] is not sufficient per se to allow us to replace the ledger by Bitcoin when used as a global setup. In particular, we cannot expect that all security statements in the global ledger-hybrid world would be preserved when using Bitcoin as a ledger. On the positive side, we provide characterizations of security statements for protocols that make use of global setups, for which the replacement is sound. Our results can be seen as a first guide on how to navigate the very tricky question of what constitutes a ``good'' global setup and how to use it in order to keep the modular protocol-design approach intact.

While unconditionally-secure quantum bit commitment (allowing both quantum computation and communication) is impossible, researchers turn to study the complexity-based one. A complexity-based canonical (non-interactive) quantum bit commitment scheme refers to a kind of scheme such that the commitment consists of just a single (quantum) message from the sender to the receiver that can be opened later by uncomputing the commit stage. In this work, we study general properties of complexity-based quantum bit commitments through the lens of canonical quantum bit commitments. Among other results, we in particular obtain the following two: 1. Any complexity-based quantum bit commitment scheme can be converted into the canonical (non-interactive) form (with its sum-binding property preserved). 2. Two flavors of canonical quantum bit commitments are equivalent; that is, canonical computationally-hiding statistically-binding quantum bit commitment exists if and only if the canonical statistically-hiding computationally-binding one exists. Combining this result with the first one, it immediately implies (unconditionally) that complexity-based quantum bit commitment is symmetric. Canonical quantum bit commitments can be based on quantum-secure one-way functions or pseudorandom quantum states. But in our opinion, the formulation of canonical quantum bit commitment is so clean and simple that itself can be viewed as a plausible complexity assumption as well. We propose to explore canonical quantum bit commitment from perspectives of both quantum cryptography and quantum complexity theory in the future.

We prove that quantum-hard one-way functions imply simulation-secure quantum oblivious transfer (QOT), which is known to suffice for secure computation of arbitrary quantum functionalities. Furthermore, our construction only makes black-box use of the quantum-hard one-way function. Our primary technical contribution is a construction of extractable and equivocal quantum bit commitments based on the black-box use of quantum-hard one-way functions in the standard model. Instantiating the Crépeau-Kilian (FOCS 1988) framework with these commitments yields simulation-secure QOT.

Permissionless blockchain systems such as Bitcoin or Ethereum are slow and expensive, since transactions are processed in a distributed network by a large set of parties. To improve on these shortcomings, a prominent approach is given by so-called 2nd-layer protocols. In these protocols parties process transactions off-chain directly between each other, thereby drastically reducing the costly and slow interaction with the blockchain. In particular, in the optimistic case, when parties behave honestly, no interaction with the blockchain is needed. One of the most popular off-chain solutions are Plasma protocols (often also called commit-chains). These protocols are orchestrated by a so-called operator that maintains the system and processes transactions between parties. Importantly, the operator is trustless, i.e., even if it is malicious users of the system are guaranteed to not lose funds. To achieve this guarantee, Plasma protocols are highly complex and require involved and expensive dispute resolution processes. This has significantly slowed down development and deployment of these systems. In this work we propose CommiTEE-- a simple and efficient Plasma system leveraging the power of trusted execution environments (TEE). Besides its simplicity, our protocol requires minimal interaction with the blockchain, thereby drastically reducing costs and improving efficiency. An additional benefit of our solution is that it allows for switching between operators, in case the main operator goes offline due to system failure, or behaving maliciously. We implemented and evaluated our system over Ethereum and show that it is at least $2$ times (and in some cases more than $16$ times) cheaper in terms of communication complexity when compared to existing Plasma implementations. Moreover, for protocols using zero-knowledge proofs (like NOCUST-ZKP), CommiTEE decreases the on-chain gas cost by a factor $\approx 19$ compared to prior solution.

Grover's search algorithm gives a quantum attack against block ciphers with query complexity $O(\sqrt{N})$ to search a keyspace of size $N$, when given a sufficient number of plaintext-ciphertext pairs. A recent result by Jaques et al. (EUROCRYPT 2020) presented the cost estimates of quantum key search attacks against AES under different security categories as defined in NIST's PQC standardization process. In this work, we extend their approach to lightweight block ciphers for the cost estimates of quantum key search attacks under circuit depth restrictions. We present quantum circuits for the lightweight block ciphers GIFT, SKINNY, and SATURNIN. We give overall cost in both the gate count and depth-times-width cost metrics, under NIST's maximum depth constraints. We also present Q# implementation of the full Grover oracles for all versions of GIFT, SKINNY, and SATURNIN for unit tests and automatic resource estimations.

We present a sub-exponential forger by using a $k$-sum algorithm against the aggregate $\Gamma$-signature, which was proposed at AsiaCCS 2019 by Zhao. Our forger is a universal forger under a key-only attack and effective in the knowledge of secret key model. We also discuss the real impact of this attack in reality with Bitcoin applications. The discussions on the real impact of the attack also highlight the significant differences between the usage of individual signatures like EC-DSA and that of aggregate signatures in the blockchain systems like Bitcoin, which might be of independent interest and could bring forth interesting questions for future investigations.

Machine learning is an important tool for analyzing large data sets, but its use on sensitive data may be limited by regulation. One solution to this problem is to perform machine learning tasks on encrypted data using homomorphic encryption, which enables arbitrary computation on encrypted data. We take a fresh look at one specific task: training a logistic regression model on encrypted data. The most important factor in the efficiency of a solution is the multiplicative depth of the homomorphic circuit. Two prior works have given circuits with multiplicative depth of five per training iteration. We optimize one of these solutions, by Han et al. [Han+18], and give a circuit with half the multiplicative depth per iteration on average, which allows us to perform twice as many training iterations in the same amount of time. In the process of improving the state-of-the-art circuit for this task, we identify general techniques to improve homomorphic circuit design for two broad classes of algorithms: iterative algorithms, and algorithms based on linear algebra over real numbers. First, we formalize the encoding scheme from [Han+18] for encoding linear algebra objects as plaintexts in the CKKS homomorphic encryption scheme. We also show how to use this encoding to homomorphically compute many basic linear algebra operations, including novel operations not discussed in prior work. This “toolkit” is generic, and can be used in any application based on linear algebra. Second, we demonstrate how generic compiler techniques for loop optimization can be used to reduce the multiplicative depth of iterative algorithms.

Saber is one of the four finalists in the ongoing NIST post-quantum cryptography standardization project. A significant portion of Saber's computation time is spent on computing polynomial multiplications in polynomial rings with powers-of-two moduli. We propose several optimization strategies for improving the performance of polynomial multiplier architectures for Saber, targeting different hardware platforms and diverse application goals. We propose two high-speed architectures that exploit the smallness of operand polynomials in Saber and can achieve great performance with a moderate area consumption. We also propose a lightweight multiplier that consumes only 541 LUTs and 301 FFs on a small Artix-7 FPGA.

HElib is a C++ open source library (see https://github.com/homenc/HElib) that implements both the BGV and CKKS fully homomorphic encryption (FHE) schemes. This document summarizes some of the basic design principles of HElib, and describes some of its fundamental algorithms and data structures in signi&#64257;cant detail. It is a work in progress, and currently focuses exclusively on the BGV scheme.

We consider leader-based Byzantine state machine replication, a.k.a. "BFT", under partial synchrony. We provide a generic solution enabling to match simultaneously, for the first time, three arguably gold standards of BFT: in two phases, with a responsive view change and a linear complexity per view. It is based on a new threshold primitive, which we call Proofs of non-Supermajority (or PnS for short). A PnS system enables players, each with an input number, to report their input to a leader, with extra hints enabling their efficient aggregation. Out of a threshold number $k$ ($=\,\! 2t{\,+\,}1$) of such reports, calling $v_\mathrm{max}$ the highest reported value, the leader can efficiently build a short proof that a threshold number of $k-t$ honest players have their inputs lower than this $v_\mathrm{max}$. As highlighted in the state of the art BFT [Abraham et al. Podc'23], any of our lightweight implementations of PnS can be plugged in their BFT, or the one of [Gelashvili et al FC'22], to bring down their complexities from quadratic to linear. Previous BFTs implicitely implemented PnS by either (i) having the leader multicasting the $k$ signed reports, so this had quadratic communication complexity, or (ii) multicasting an aggregate signature on the reports, with verification complexity of $k+1$ pairings, so this had a total quadratic computation complexity. To match our linear complexity claim, we introduce a very simple constant-sized and constant-verification implementation of PnS, built from any threshold (or multi-) signature scheme. We then bring further optimizations by introducing the following tools of possible independent interest: (1) a simple and general optimization to BFTs, which applies to any view without a hidden lock. It removes the need for sending and verifying a PnS. Previous optimizations applied to a narrower set of views, essentially, those for which the leader of the previous one was honest and enjoyed synchrony; (2) a simple compiler from any multisignature scheme, into an aggregate signature scheme of a special-purpose type. It operates over tagged messages, each key can sign at most one message with a given tag.

Governments and policy makers are finding it difficult to curb the enormous spread of pandemic Covid-19 till the vaccine is invented and becomes available for use. When a person is detected to be infected with Novel coronavirus, the task of identifying the persons who have come across the victim in past fortnight is a challenging task. Identifying these contact persons manually is a hilarious task and often yields incomplete data. Some governments have used digital technology for contact tracing but it is prone to compromise privacy of citizens. In this paper, we propose to use blockchain for recording every transaction in a secure manner that involves communications between users who are equipped with cloud-enabled body area networks. Whenever an user is tested coronavirus positive, the health officials and concerned administration immediately finds only those blockchain transaction records corresponding to the infected persons to identify the contact tracings in the past fortnight. Further, if a contact person is suffering from high temparature that is also detected automatically by the proposed system. This proposed system will help authoroties immensely to quickly quarantine the contacts of Covid-19 cases and curb the spread of coronavirus beyond a limit while maintaining the privacy of users.

Multi-signatures are used to attest that a fixed collection of $n$ parties, represented by their respective public keys, have all signed a given message. An emerging application of multi-signatures is to be found in consensus protocols to attest that a qualified subset of a global set of $n$ validators have reached agreement. In this paper, we point out that the traditional security model for multi-signatures is insufficient for this new application, as it assumes that every party in the set participates in the multi-signature computation phase and is honest. None of these assumptions hold in the typical adversarial scenarios in consensus protocols (aka. byzantine agreement). We address this by introducing a new multi-signature variant called robust subgroup multi-signatures, whereby any eligible subgroup of signers from the global set can produce a multi-signature on behalf of the group, even in the presence of a byzantine adversary. We provide syntax and security definitions for the new variant. We argue that existing unforgeability security proofs for multi-signatures do not carry over to the consensus setting; a consequence of this observation is that many multi-signature based consensus protocols lack a rigorous security proof for correctness. To remedy this we propose several constructions which we prove secure under widely held cryptographic assumptions using our newly introduced formal definitions and also improve upon multi-signature computation time. Finally, we report on benchmarks from a proof-of-concept implementation.

ElectionGuard is an open source set of software components and specifications from Microsoft designed to allow the modification of a number of different e-voting protocols and products to produce public evidence (transcripts) which anyone can verify. The software uses ElGamal, homomorphic tallying and sigma protocols to enable public scrutiny without adversely affecting privacy. Some components have been formally verified (machine-checked) to be free of certain software bugs but there was no formal verification of their cryptographic security. Here, we present a machine-checked proof of the verifiability guarantees of the transcripts produced and verified according to the ElectionGuard specification. We have also extracted an executable version of the verifier specification, which we proved to be secure, and used it to verify election transcripts produced by ElectionGuard. Our results show that our implementation is of similar efficiency to existing implementations.

Blockchain has the potential to accelerate the worldwide deployment of an emissions trading system (ETS) and improve the efficiency of existing systems. In this paper, we present a model for a permissioned blockchain implementation based on the successful European Union (EU) ETS and discuss its potential advantages over existing technology. The proposed ETS model is both backward compatible and future-proof, characterised by interconnectedness, transparency, tamper-resistance and continuous liquidity. Further, we identify key challenges to implementation of blockchain in ETS, as well as areas of future work required to enable a fully decentralised blockchain-based ETS.

Revocable identity-based encryption (RIBE) is an extension of identity-based encryption (IBE) and it supports efficient revocation of private keys. In the past, many efficient RIBE schemes have been proposed, but research on efficiently delegating the generation of update keys to a cloud server is somewhat insufficient. In this paper, we newly introduce the concept of delegated RIBE (DRIBE) that can delegate the generation of update keys to the semi-trusted cloud server and define the security models of DRIBE. Next, we propose a DRIBE scheme by generically combining a hierarchical IBE (HIBE) scheme, an identity-based broadcast encryption (IBBE) scheme, and a collision-resistant hash function. In addition, we propose a DRIBE-INC scheme that generates an occasional base update key and a periodic incremental update key to reduce the size of the update key in our DRIBE scheme.

A cryptographic protocol (CP) is a distributed algorithm designed to provide a secure communication in an insecure environment. CPs are used, for example, in electronic payments, electronic voting procedures, database access systems, etc. Errors in the CPs can lead to great financial and social damage, therefore it is necessary to use mathematical methods to justify the correctness and safety of the CPs. In this paper, a new mathematical model of a CP is introduced, which allows one to describe both the CPs and their properties. It is shown how, on the basis of this model, it is possible to solve the problems of verification of CPs.

Super-spreader events where one person infects many others have been a driving force of the Covid-19 pandemic. Such events often happen indoors, such as in restaurants, at choir practice or in gyms. Many systems for automated contact tracing (ACT) have been proposed, which will warn a user when they have been in proximity to an infected person. These generally fail to detect potential super-spreader events as only users who have come in close contact with the infected person, but not others who also visited the same location, are warned. Other approaches allow users to check into locations or venues, but these require user interaction. We propose two designs how broadcast-based ACT systems can be enhanced to utilize location-specific information without the need for GPS traces or scanning of QR codes. This makes it possible to alert attendees of a potential super-spreader event while still remaining private. Our first design relies on cooperating lighthouses which cover a large area and send out pseudonyms. These are recorded by visitors and published by the health authority (HA) in case of an infection. The second design has lighthouses actively communicating with HAs after retrospectively detecting an infected visitor to warn everyone whose stay overlapped.

The advent of quantum computers is a threat to most currently deployed cryptographic primitives. Among these, zero-knowledge proofs play an important role, due to their numerous applications. The primitives and protocols presented in this work base their security on the difficulty of solving the Rank Syndrome Decoding (RSD) problem. This problem is believed to be hard even in the quantum model. We first present a perfectly binding commitment scheme. Using this scheme, we are able to build an interactive zero-knowledge proof to prove: the knowledge of a valid opening of a committed value, and that the valid openings of three committed values satisfy a given linear relation, and, more generally, any bitwise relation. With the above protocols it becomes possible to prove the relation of two committed values for an arbitrary circuit, with quasi-linear communication complexity and a soundness error of 2/3. To our knowledge, this is the first quantum resistant zero-knowledge protocol for arbitrary circuits based on the RSD problem. An important contribution of this work is the selection of a set of parameters, and an a full implementation, both for our proposal in the rank metric and for the original LPN based one by Jain et. al in the Hamming metric, from which we took the inspiration. Beside demonstrating the practicality of both constructions, we provide evidence of the convenience of rank metric, by reporting performance benchmarks and a detailed comparison.

We construct the first constant-round protocols for secure quantum computation in the two-party (2PQC) and multi-party (MPQC) settings with security against malicious adversaries. Our protocols are in the common random string (CRS) model. - Assuming two-message oblivious transfer (OT), we obtain (i) three-message 2PQC, and (ii) five-round MPQC with only three rounds of online (input-dependent) communication; such OT is known from quantum-hard Learning with Errors (QLWE). - Assuming sub-exponential hardness of QLWE, we obtain (i) three-round 2PQC with two online rounds and (ii) four-round MPQC with two online rounds. - When only one (out of two) parties receives output, we achieve minimal interaction (two messages) from two-message OT; classically, such protocols are known as non-interactive secure computation (NISC), and our result constitutes the first maliciously-secure quantum NISC. Additionally assuming reusable malicious designated-verifier NIZK arguments for NP (MDV-NIZKs), we give the first MDV-NIZK for QMA that only requires one copy of the quantum witness. Finally, we perform a preliminary investigation into two-round secure quantum computation where each party must obtain output. On the negative side, we identify a broad class of simulation strategies that suffice for classical two-round secure computation that are unlikely to work in the quantum setting. Next, as a proof-of-concept, we show that two-round secure quantum computation exists with respect to a quantum oracle.

Most state machine replication protocols are either based on the 40-years-old Byzantine Fault Tolerance (BFT) theory or the more recent Nakamoto’s longest chain design. Longest chain protocols, designed originally in the Proof-of-Work (PoW) setting, are available under dynamic participation, but has probabilistic confirmation with long latency dependent on the security parameter. BFT protocols, designed for the permissioned setting, has fast deterministic confirmation, but assume a fixed number of nodes always online. We present a new construction which combines a longest chain protocol and a BFT protocol to get the best of both worlds. Using this construction, we design TaiJi, the first dynamically available PoW protocol which has almost deterministic confirmation with latency independent of the security parameter. In contrast to previous hybrid approaches which use a single longest chain to sample participants to run a BFT protocol, our native PoW construction uses many independent longest chains to sample propose actions and vote actions for the BFT protocol. This design enables TaiJi to inherit the full dynamic availability of Bitcoin, as well as its full unpredictability, making it secure against fully-adaptive adversaries with up to 50% of online hash power.

In the universal blind quantum computation problem, a client wants to make use of a single quantum server to evaluate $C|0\rangle$ where $C$ is an arbitrary quantum circuit while keeping $C$ secret. The client's goal is to use as few resources as possible. This problem, first raised by Broadbent, Fitzsimons and Kashefi [FOCS09, arXiv:0807.4154], has become fundamental to the study of quantum cryptography, not only because of its own importance, but also because it provides a testbed for new techniques that can be later applied to related problems (for example, quantum computation verification). Known protocols on this problem are mainly either information-theoretically (IT) secure or based on trapdoor assumptions (public key encryptions). In this paper we study how the availability of symmetric-key primitives, modeled by a random oracle, changes the complexity of universal blind quantum computation. We give a new universal blind quantum computation protocol. Similar to previous works on IT-secure protocols (for example, BFK [FOCS09, arXiv:0807.4154]), our protocol can be divided into two phases. In the first phase the client prepares some quantum gadgets with relatively simple quantum gates and sends them to the server, and in the second phase the client is entirely classical -- it does not even need quantum storage. Crucially, the protocol's first phase is succinct, that is, its complexity is independent of the circuit size. Given the security parameter $\kappa$, its complexity is only a fixed polynomial of $\kappa$, and can be used to evaluate any circuit (or several circuits) of size up to a subexponential of $\kappa$. In contrast, known schemes either require the client to perform quantum computations that scale with the size of the circuit [FOCS09, arXiv:0807.4154], or require trapdoor assumptions [Mahadev, FOCS18, arXiv:1708.02130].

Cloud auditing with ownership transfer is a provable data possession scheme meeting verifiability and transferability simultaneously. In particular, not only cloud data can be transferred to other cloud clients, but also tags for integrity verification can be transferred to new data owners. More concretely, it requires that tags belonging to the old owner can be transformed into that of the new owner by replacing the secret key for tag generation while verifiability still remains. We found that existing solutions are less efficient due to the huge communication overhead linear with the number of tags. In this paper, we propose a secure auditing protocol with efficient ownership transfer for cloud data. Specifically, we sharply reduce the communication overhead produced by ownership transfer to be independent of the number of tags, making it with a constant size. Meanwhile, the computational cost during this process on both transfer parties is constant as well.

The Learning with Errors (LWE) problem is one of the main mathematical foundations of post-quantum cryptography. One of the main groups of algorithms for solving LWE is the Blum-Kalai-Wasserman (BKW) algorithm. This paper presents new improvements for BKW-style algorithms for solving LWE instances. We target minimum concrete complexity and we introduce a new reduction step where we partially reduce the last position in an iteration and finish the reduction in the next iteration, allowing non-integer step sizes. We also introduce a new procedure in the secret recovery by mapping the problem to binary problems and applying the Fast Walsh Hadamard Transform. The complexity of the resulting algorithm compares favourably to all other previous approaches, including lattice sieving. We additionally show the steps of implementing the approach for large LWE problem instances. The core idea here is to overcome RAM limitations by using large file-based memory.

Sharding is an approach to designing a highly scalable blockchain. A sharded blockchain achieves parallelism by dividing consensus nodes (validators) into groups called shards and making them process different transactions in each shard. In this paper, we economically analyze users’ behavior on sharded blockchains and identify a phenomenon that users’ accounts and smart contracts eventually get concentrated in a few shards, making shard loads unfair. This phenomenon leads to bad user experiences, such as delays in transaction inclusions and increased transaction fees. To solve the above problem, we propose a load balancing framework in sharded blockchains in which accounts and contracts are frequently reassigned into shards to reduce the difference of loads between shards. We formulate the contract reassignment as an optimization problem and present the algorithm to solve it. Further, we apply the framework to an existing sharding design (Ethereum 2.0) and modify the protocol to do load balancing. Finally, we simulate the protocol and observe smaller transaction delays and fees.