Papers updated in last 31 days (210 results)

Last updated:  2022-08-08
DiSSECT: Distinguisher of Standard & Simulated Elliptic Curves via Traits
Vladimir Sedlacek, Vojtech Suchanek, Antonin Dufka, Marek Sys, and Vashek Matyas
It can be tricky to trust elliptic curves standardized in a non-transparent way. To rectify this, we propose a systematic methodology for analyzing curves and statistically comparing them to the expected values of a large number of generic curves with the aim of identifying any deviations in the standard curves. For this purpose, we put together the largest publicly available database of standard curves. To identify unexpected properties of standard generation methods and curves, we simulate over 250 000 curves by mimicking the generation process of four standards. We compute 22 different properties of curves and analyze them with automated methods to pinpoint deviations in standard curves, pointing to possible weaknesses.
Last updated:  2022-08-08
An algebraic attack to the Bluetooth stream cipher E0
Roberto La Scala, Sergio Polese, Sharwan K. Tiwari, and Andrea Visconti
In this paper we study the security of the Bluetooth stream cipher E0 from the viewpoint it is a “difference stream cipher”, that is, it is defined by a system of explicit difference equations over the finite field GF(2). This approach highlights some issues of the Bluetooth encryption such as the invertibility of its state transition map, a special set of 14 bits of its 132-bit state which when guessed implies linear equations among the other bits and finally a small number of spurious keys, with 83 guessed bits, which are compatible with a keystream of about 60 bits. Exploiting these issues, we implement an algebraic attack using Gröbner bases, SAT solvers and Binary Decision Diagrams. Testing activities suggest that the version based on Gröbner bases is the best one and it is able to attack E0 in about 2^79 seconds on an Intel i9 CPU. To the best of our knowledge, this work improves any previous attack based on a short keystream, hence fitting with Bluetooth specifications.
Last updated:  2022-08-08
Secure and Private Source Coding with Private Key and Decoder Side Information
Onur Gunlu, Rafael F. Schaefer, Holger Boche, and H. Vincent Poor
The problem of secure source coding with multiple terminals is extended by considering a remote source whose noisy measurements are the correlated random variables used for secure source reconstruction. The main additions to the problem include 1) all terminals noncausally observe a noisy measurement of the remote source; 2) a private key is available to all legitimate terminals; 3) public communication link between the encoder and decoder is rate-limited; and 4) secrecy leakage to the eavesdropper is measured with respect to the encoder input, whereas privacy leakage is measured with respect to the remote source. Exact rate regions are characterized for a lossy source coding problem with a private key, remote source, and decoder side information under security, privacy, communication, and distortion constraints. By replacing the distortion constraint with a reliability constraint, we obtain the exact rate region also for the lossless case. Furthermore, the lossy rate region for scalar discrete-time Gaussian sources and channels is established.
Last updated:  2022-08-08
Towards Practical Homomorphic Time-Lock Puzzles: Applicability and Verifiability
Yi Liu, Qi Wang, and Siu-Ming Yiu
Time-lock puzzle schemes allow one to encrypt messages for the future. More concretely, one can efficiently generate a time-lock puzzle for a secret/solution $s$, such that $s$ remains hidden until a specified time $T$ has elapsed, even for any parallel adversaries. However, since computation on secrets within multiple puzzles can be performed only when \emph{all} of these puzzles are solved, the usage of classical time-lock puzzles is greatly limited. Homomorphic time-lock puzzle (HTLP) schemes were thus proposed to allow evaluating functions over puzzles directly without solving them. However, although efficient HTLP schemes exist, more improvements are still needed for practicability. In this paper, we improve HTLP schemes to broaden their application scenarios from the aspects of \emph{applicability} and \emph{verifiability}. In terms of applicability, we design the \emph{first} multiplicatively HTLP scheme with the solution space over $\mathbb{Z}_n^*$, which is more expressible than the original one, \eg representing integers. Then, to fit HTLP into scenarios requiring verifiability that is missing in existing schemes, we propose three \emph{simple} and \emph{fast} protocols for both the additively HTLP scheme and our multiplicatively HTLP scheme, respectively. The first two protocols allow a puzzle solver to convince others of the correctness of the solution or the invalidity of the puzzle so that others do not need to solve the puzzle themselves. The third protocol allows a puzzle generator to prove the validity of his puzzles. It is shown that a puzzle in our scheme is only $1.25$KB, and one multiplication on puzzles takes simply $0.01$ms. Meanwhile, the overhead of each protocol is less than $0.6$KB in communication and $40$ms in computation. Hence, HTLP still demonstrates excellent efficiency in both communication and computation with these versatile properties.
Last updated:  2022-08-08
Roulette: A Diverse Family of Feasible Fault Attacks on Masked Kyber
Jeroen Delvaux
At Indocrypt 2021, Hermelink, Pessl, and Pöppelmann presented a fault attack against Kyber in which a system of linear inequalities over the private key is generated and solved. The attack requires a laser and is, understandably, demonstrated with simulations—not actual equipment. We facilitate and diversify the attack in four ways, thereby admitting cheaper and more forgiving fault-injection setups. Firstly, the attack surface is enlarged: originally, the two input operands of the ciphertext comparison are covered, and we additionally cover re-encryption modules such as binomial sampling and butterflies in the last layer of the inverse number-theoretic transform (INTT). This extra surface also allows an attacker to bypass the custom countermeasure that was proposed in the Indocrypt paper. Secondly, the fault model is relaxed: originally, precise bit flips are required, and we additionally support set-to-0 faults, random faults, arbitrary bit flips, and instruction skips. Thirdly, masking and blinding methods that randomize intermediate variables kindly help our attack, whereas the IndoCrypt attack is like most other fault attacks either hindered or unaltered by countermeasures against passive side-channel analysis (SCA). Randomization helps because we randomly fault intermediate prime-field elements until a desired set of values is hit. If these prime-field elements are represented on a circle, which is a common visualization, our attack is analogous to spinning a roulette wheel until the ball lands in a desired set of pockets. Hence, the nickname. Fourthly, we accelerate and improve the error tolerance of solving the system of linear inequalities: run times of roughly 100 minutes are reduced to roughly one minute, and inequality error rates of roughly 1% are relaxed to roughly 25%. Benefiting from the four advances above, we use a reasonably priced ChipWhisperer board to break a masked implementation of Kyber running on an ARM Cortex-M4 through clock glitching.
Last updated:  2022-08-08
Orion: Zero Knowledge Proof with Linear Prover Time
Tiancheng Xie, Yupeng Zhang, and Dawn Song
Zero-knowledge proof is a powerful cryptographic primitive that has found various applications in the real world. However, existing schemes with succinct proof size suffer from a high overhead on the proof generation time that is super-linear in the size of the statement represented as an arithmetic circuit, limiting their efficiency and scalability in practice. In this paper, we present Orion, a new zero-knowledge argument system that achieves $O(N)$ prover time of field operations and hash functions and $O(\log^2 N)$ proof size. Orion is concretely efficient and our implementation shows that the prover time is 3.09s and the proof size is 1.5MB for a circuit with $2^{20}$ multiplication gates. The prover time is the fastest among all existing succinct proof systems, and the proof size is an order of magnitude smaller than a recent scheme proposed in Golovnev et al. 2021. In particular, we develop two new techniques leading to the efficiency improvement. (1) We propose a new algorithm to test whether a random bipartite graph is a lossless expander graph or not based on the densest subgraph algorithm. It allows us to sample lossless expanders with an overwhelming probability. The technique improves the efficiency and/or security of all existing zero-knowledge argument schemes with a linear prover time. The testing algorithm based on densest subgraph may be of independent interest for other applications of expander graphs. (2) We develop an efficient proof composition scheme, code switching, to reduce the proof size from square root to polylogarithmic in the size of the computation. The scheme is built on the encoding circuit of a linear code and shows that the witness of a second zero-knowledge argument is the same as the message in the linear code. The proof composition only introduces a small overhead on the prover time.
Last updated:  2022-08-08
Improved Plantard Arithmetic for Lattice-based Cryptography
Junhao Huang, Jipeng Zhang, Haosong Zhao, Zhe Liu, Ray C. C. Cheung, Çetin Kaya Koç, and Donglong Chen
This paper presents an improved Plantard's modular arithmetic (Plantard arithmetic) tailored for Lattice-Based Cryptography (LBC). Based on the improved Plantard arithmetic, we present faster implementations of two LBC schemes, Kyber and NTTRU, running on Cortex-M4. The intrinsic advantage of Plantard arithmetic is that one multiplication can be saved from the modular multiplication of a constant. However, the original Plantard arithmetic is not very practical in LBC schemes because of the limitation on the unsigned input range. In this paper, we improve the Plantard arithmetic and customize it for the existing LBC schemes with theoretical proof. The improved Plantard arithmetic not only inherits its aforementioned advantage but also accepts signed inputs, produces signed output, and enlarges its input range compared with the original design. Moreover, compared with the state-of-the-art Montgomery arithmetic, the improved Plantard arithmetic has a larger input range and smaller output range, which allows better lazy reduction strategies during the NTT/INTT implementation in current LBC schemes. All these merits make it possible to replace the Montgomery arithmetic with the improved Plantard arithmetic in LBC schemes on some platforms. After applying this novel method to Kyber and NTTRU schemes using 16-bit NTT on Cortex-M4 devices, we show that the proposed design outperforms the known fastest implementation that uses Montgomery and Barrett arithmetic. Specifically, compared with the state-of-the-art Kyber implementation, applying the improved Plantard arithmetic in Kyber results in a speedup of 25.02% and 18.56% for NTT and INTT, respectively. Compared with the reference implementation of NTTRU, our NTT and INTT achieve speedup by 83.21% and 78.64%, respectively. As for the LBC KEM schemes, we set new speed records for Kyber and NTTRU running on Cortex-M4.
Last updated:  2022-08-07
Generic Construction of UC-Secure Oblivious Transfer
Olivier Blazy and Céline Chevalier
We show how to construct a completely generic UC-secure oblivious transfer scheme from a collision-resistant chameleon hash scheme (CH) and a CCA encryption scheme accepting a smooth projective hash function (SPHF). Our work is based on the work of Abdalla et al. at Asiacrypt 2013, where the authors formalize the notion of SPHF-friendly commitments, i.e. accepting an SPHF on the language of valid commitments (to allow implicit decommitment), and show how to construct from them a UC-secure oblivious transfer in a generic way. But Abdalla et al. only gave a DDH-based construction of SPHF-friendly commitment schemes, furthermore highly relying on pairings. In this work, we show how to generically construct an SPHF-friendly commitment scheme from a collision-resistant CH scheme and an SPHF-friendly CCA encryption scheme. This allows us to propose an instantiation of our schemes based on the DDH, as efficient as that of Abdalla et al., but without requiring any pairing. Interestingly, our generic framework also allows us to propose an instantiation based on the learning with errors (LWE) assumption. For the record, we finally propose a last instantiation based on the decisional composite residuosity (DCR) assumption.
Last updated:  2022-08-07
Guide to Fully Homomorphic Encryption over the [Discretized] Torus
Marc Joye
First posed as a challenge in 1978 by Rivest et al., fully homomorphic encryption—the ability to evaluate any function over encrypted data— was only solved in 2009 in a breakthrough result by Gentry (Commun. ACM, 2010). After a decade of intense research, practical solutions have emerged and are being pushed for standardization. This guide is intended to practitioners. It explains the inner-workings of TFHE, a torus-based fully homomorphic encryption scheme. More exactly, it describes its implementation on a discretized version of the torus. It also explains in detail the technique of the programmable bootstrapping.
Last updated:  2022-08-07
Uncle Maker: (Time)Stamping Out The Competition in Ethereum
Aviv Yaish, Gilad Stern, and Aviv Zohar
We present an attack on Ethereum's consensus mechanism which can be used by miners to obtain consistently higher mining rewards compared to the honest protocol. This attack is novel in that it does not entail withholding blocks or any behavior which has a non-zero probability of earning less than mining honestly, in contrast with the existing literature. This risk-less attack relies instead on manipulating block timestamps, and carefully choosing whether and when to do so. We present this attack as an algorithm, which we then analyze to evaluate the revenue a miner obtains from it, and its effect on a miner's absolute and relative share of the main-chain blocks. The attack allows an attacker to replace competitors' main-chain blocks after the fact with a block of its own, thus causing the replaced block's miner to lose all transactions fees for the transactions contained within the block, which will be demoted from the main-chain. This block, although ``kicked-out'' of the main-chain, will still be eligible to be referred to by other main-chain blocks, thus becoming what is commonly called in Ethereum an uncle. We proceed by defining multiple variants of this attack, and assessing whether any of these attacks has been performed in the wild. Surprisingly, we find that this is indeed true, making this the first case of a confirmed consensus-level manipulation performed on a major cryptocurrency. Additionally, we implement a variant of this attack as a patch for geth, Ethereum's most popular client, making it the first consensus-level attack on Ethereum which is implemented as a patch. Finally, we suggest concrete fixes for Ethereum's protocol and implemented them as a patch for geth which can be adopted quickly and mitigate the attack and its variants.
Last updated:  2022-08-07
Physically Related Functions: A New Paradigm for Light-weight Key-Exchange
Durba Chatterjee, Harishma Boyapally, Sikhar Patranabis, Urbi Chatterjee, Debdeep Mukhopadhyay, and Aritra Hazra
In this paper, we propose a novel concept named Physically Related Function(PReF) which are devices with hardware roots of trust. It enables secure key-exchange with no pre-established/embedded secret keys. This work is motivated by the need to perform key-exchange between lightweight resource-constrained devices. We present a proof-of-concept realization of our contributions in hardware using FPGAs.
Last updated:  2022-08-07
Masked-degree SIDH
Tomoki Moriya
Isogeny-based cryptography is one of the candidates for post-quantum cryptography. SIDH is a compact and efficient isogeny-based key exchange, and SIKE, which is the SIDH-based key encapsulation mechanism, remains the NIST PQC Round 4. However, by the brilliant attack provided by Castryck and Decru, the original SIDH is broken in polynomial time (with heuristics). To break the original SIDH, there are three important pieces of information in the public key: information about the endomorphism ring of a starting curve, some image points under a cyclic hidden isogeny, and the degree of the isogeny. In this paper, we proposed the new isogeny-based scheme named \textit{masked-degree SIDH}. This scheme is the variant of SIDH that masks most information about degrees of hidden isogenies, and the first trial against Castryck--Decru attack. The main idea to cover degrees is to use many primes to compute isogenies that allow the degree to be more flexible. Though the size of the prime $p$ for this scheme is slightly larger than that of SIDH, this scheme resists current attacks using degrees of isogenies like the attack of Castryck and Decru. The most effective attack for masked-degree SIDH has $\tilde{O}(p^{1/(8\log_2{(\log_2{p})})})$ time complexity with classical computers and $\tilde{O}(p^{1/(16\log_2{(\log_2{p})})})$ time complexity with quantum computers in our analysis.
Last updated:  2022-08-06
Time-Deniable Signatures
Gabrielle Beck, Arka Rai Choudhuri, Matthew Green, Abhishek Jain, and Pratyush Ranjan Tiwari
In this work we propose time-deniable signatures (TDS), a new primitive that facilitates deniable authentication in protocols such as DKIM-signed email. As with traditional signatures, TDS provide strong authenticity for message content, at least for a sender-chosen period of time. Once this time period has elapsed, however, time-deniable signatures can be forged by any party who obtains a signature. This forgery property ensures that signatures serve a useful authentication purpose for a bounded time period, while also allowing signers to plausibly disavow the creation of older signed content. Most critically, and unlike many past proposals for deniable authentication, TDS do not require interaction with the receiver or the deployment of any persistent cryptographic infrastructure or services beyond the signing process (e.g., APIs to publish secrets or author timestamp certificates.) We first investigate the security definitions for time-deniability, demonstrating that past definitional attempts are insufficient (and indeed, allow for broken signature schemes.) We then propose an efficient construction of TDS based on well-studied assumptions.
Last updated:  2022-08-06
PERKS: Persistent and Distributed Key Acquisition for Secure Storage from Passwords
Gareth T. Davies and Jeroen Pijnenburg
We investigate how users of instant messaging (IM) services can acquire strong encryption keys to back up their messages and media with strong cryptographic guarantees. Many IM users regularly change their devices and use multiple devices simultaneously, ruling out any long-term secret storage. Extending the end-to-end encryption guarantees from just message communication to also incorporate backups has so far required either some trust in an IM or outsourced storage provider, or use of costly third-party encryption tools with unclear security guarantees. Recent works have proposed solutions for password-protected key material, however all require one or more servers to generate and/or store per-user information, inevitably invoking a cost to the users. We define distributed key acquisition (DKA) as the primitive for the task at hand, where a user interacts with one or more servers to acquire a strong cryptographic key, and both user and server are required to store as little as possible. We present a construction framework that we call PERKS---Password-based Establishment of Random Keys for Storage---providing efficient, modular and simple protocols that utilize Oblivious Pseudorandom Functions (OPRFs) in a distributed manner with minimal storage by the user (just the password) and servers (a single global key for all users). Along the way we introduce a formal treatment of DKA, and provide proofs of security for our constructions in their various flavours. Our approach enables key rotation by the OPRF servers, and for this we incorporate updatable encryption. Finally, we show how our constructions fit neatly with recent research on encrypted outsourced storage to provide strong security guarantees for the outsourced ciphertexts.
Last updated:  2022-08-06
Analysing the HPKE Standard
Joël Alwen, Bruno Blanchet, Eduard Hauck, Eike Kiltz, Benjamin Lipp, and Doreen Riepel
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).
Last updated:  2022-08-06
Coefficient Grouping: Breaking Chaghri and More
Fukang Liu, Ravi Anand, Libo Wang, Willi Meier, and Takanori Isobe
We propose an efficient technique called coefficient grouping to evaluate the algebraic degree of the FHE-friendly cipher Chaghri, which has been accepted for ACM CCS 2022. It is found that the algebraic degree increases linearly rather than exponentially. As a consequence, we can construct a 13-round distinguisher with time and data complexity of $2^{63}$ and mount a 13.5-round key-recovery attack with time complexity of about $2^{119.6}$. In particular, a higher-order differential attack on 8 rounds of Chaghri can be achieved with time and data complexity of $2^{38}$. Hence, it indicates that the full 8 rounds are far from being secure. Furthermore, we also demonstrate the application of our coefficient grouping technique to the design of secure cryptographic components. As a result, a countermeasure is found for Chaghri and it has little overhead compared with the original design. Since more and more symmetric primitives defined over a large finite field are emerging, we believe our new technique can have more applications in the future research.
Last updated:  2022-08-06
Public Key Authenticated Encryption with Keyword Search from LWE
Leixiao Cheng and Fei Meng
Public key encryption with keyword search (PEKS) inherently suffers from the inside keyword guessing attack. To resist against this attack, Huang et al. proposed the public key authenticated encryption with keyword search (PAEKS), where the sender not only encrypts a keyword, but also authenticates it. To further resist against quantum attacks, Liu et al. proposed a generic construction of PAEKS and the first quantum-resistant PAEKS instantiation based on lattices. Later, Emura pointed out some issues in Liu et al.'s construction and proposed a new generic construction of PAEKS. The basic construction methodology of Liu et al. and Emura is the same, i.e., each keyword is converted into an extended keyword using the shared key calculated by a word-independent smooth projective hash functions (SPHF), and PEKS is used for the extended keyword. In this paper, we first analyze the schemes of Liu et al. and Emura, and point out some issues regarding their construction and security model. In short, in their lattice-based instantiations, the sender and receiver use a lattice-based word independent SPHF to compute the same shared key to authenticate keywords, leading to a super-polynomial modulus $q$; their generic constructions need a trusted setup assumption or the designated-receiver setting; Liu et al. failed to provide convincing evidence that their scheme satisfies their claimed security. Then, we propose two new lattice-based PAEKS schemes with totally different construction methodology from Liu et al. and Emura. Specifically, in our PAEKS schemes, instead of using the shared key calculated by SPHF, the sender and receiver achieve keyword authentication by using their own secret key to sample a set of short vectors related to the keyword. In this way, the modulus $q$ in our schemes could be of polynomial size, which results in much smaller size of the public key, ciphertext and trapdoor. In addition, our schemes need neither a trusted setup assumption nor the designated-receiver setting. Finally, our schemes can be proven secure in stronger security model, and thus provide stronger security guarantee for both ciphertext privacy and trapdoor privacy.
Last updated:  2022-08-05
One Server for the Price of Two: Simple and Fast Single-Server Private Information Retrieval
Alexandra Henzinger, Matthew M. Hong, Henry Corrigan-Gibbs, Sarah Meiklejohn, and Vinod Vaikuntanathan
We present SimplePIR, the fastest private information retrieval (PIR) scheme known to date. SimplePIR is a single-server PIR scheme, whose security holds under the learning-with-errors assumption. To answer a client’s PIR query, the SimplePIR server performs one 32-bit multiplication and one 32-bit addition per database byte. SimplePIR achieves 6.5 GB/s/core server throughput, which is 7% faster than the fastest two-server PIR schemes (which require non-colluding servers). SimplePIR has relatively large communication costs: to make queries to a 1 GB database, the client must download a 124 MB “hint” about the database contents; thereafter, the client may make an unbounded number of queries, each requiring 242 KB of communication. We present a second single-server scheme, DoublePIR, that shrinks the hint to 16 MB at the cost of slightly higher per-query communication (345 KB) and slightly lower throughput (5.2 GB/s/core). Finally, we apply our PIR schemes, together with a new data structure for approximate set membership, to the problem of private auditing in Certificate Transparency. We achieve a strictly stronger notion of privacy than Google Chrome’s current approach with a modest, 13× larger communication overhead.
Last updated:  2022-08-05
Quantum Cryptanalysis of $5$ rounds Feistel schemes and Benes schemes
Maya Chartouny, Jacques Patarin, and Ambre Toulemonde
In this paper, we provide new quantum cryptanalysis results on $5$ rounds (balanced) Feistel schemes and on Benes schemes. More precisely, we give an attack on $5$ rounds Feistel schemes in $\Theta(2^{2n/3})$ quantum complexity and an attack on Benes schemes in $\Theta(2^{2n/3})$ quantum complexity, where $n$ is the number of bits of the internel random functions.
Last updated:  2022-08-05
An efficient key recovery attack on SIDH (preliminary version)
Wouter Castryck and Thomas Decru
We present an efficient key recovery attack on the Supersingular Isogeny Diffie-Hellman protocol (SIDH), based on a "glue-and-split" theorem due to Kani. Our attack exploits the existence of a small non-scalar endomorphism on the starting curve, and it also relies on the auxiliary torsion point information that Alice and Bob share during the protocol. Our Magma implementation breaks the instantiation SIKEp434, which aims at security level 1 of the Post-Quantum Cryptography standardization process currently ran by NIST, in about one hour on a single core. This is a preliminary version of a longer article in preparation.
Last updated:  2022-08-05
Correlated Pseudorandomness from Expand-Accumulate Codes
Elette Boyle, Geoffroy Couteau, Niv Gilboa, Yuval Ishai, Lisa Kohl, Nicolas Resch, and Peter Scholl
A pseudorandom correlation generator (PCG) is a recent tool for securely generating useful sources of correlated randomness, such as random oblivious transfers (OT) and vector oblivious linear evaluations (VOLE), with low communication cost. We introduce a simple new design for PCGs based on so-called expand-accumulate codes, which first apply a sparse random expander graph to replicate each message entry, and then accumulate the entries by computing the sum of each prefix. Our design offers the following advantages compared to state-of-the-art PCG constructions: - Competitive concrete efficiency backed by provable security against relevant classes of attacks; - An offline-online mode that combines near-optimal cache-friendliness with simple parallelization; - Concretely efficient extensions to pseudorandom correlation functions, which enable incremental generation of new correlation instances on demand, and to new kinds of correlated randomness that include circuit-dependent correlations. To further improve the concrete computational cost, we propose a method for speeding up a full-domain evaluation of a puncturable pseudorandom function (PPRF). This is independently motivated by other cryptographic applications of PPRFs.
Last updated:  2022-08-05
Dynamic Local Searchable Symmetric Encryption
Brice Minaud and Michael Reichle
In this article, we tackle for the first time the problem of dynamic memory-efficient Searchable Symmetric Encryption (SSE). In the term "memory-efficient" SSE, we encompass both the goals of local SSE, and page-efficient SSE. The centerpiece of our approach is a new connection between those two goals. We introduce a map, called the Generic Local Transform, which takes as input a page-efficient SSE scheme with certain special features, and outputs an SSE scheme with strong locality properties. We obtain several results. 1. First, we build a dynamic SSE scheme with storage efficiency $O(1)$ and page efficiency only $\tilde{O}(\log \log (N/p))$, where $p$ is the page size, called LayeredSSE. The main technique behind LayeredSSE is a new weighted extension of the two-choice allocation process, of independent interest. 2. Second, we introduce the Generic Local Transform, and combine it with LayeredSSE to build a dynamic SSE scheme with storage efficiency $O(1)$, locality $O(1)$, and read efficiency $\tilde{O}(\log\log N)$, under the condition that the longest list is of size $O(N^{1-1/\log \log \lambda})$. This matches, in every respect, the purely static construction of Asharov et al. from STOC 2016: dynamism comes at no extra cost. 3. Finally, by applying the Generic Local Transform to a variant of the Tethys scheme by Bossuat et al. from Crypto 2021, we build an unconditional static SSE with storage efficiency $O(1)$, locality $O(1)$, and read efficiency $O(\log^\varepsilon N)$, for an arbitrarily small constant $\varepsilon > 0$. To our knowledge, this is the construction that comes closest to the lower bound presented by Cash and Tessaro at Eurocrypt 2014.
Last updated:  2022-08-05
Nonce-Misuse Resilience of Romulus-N and GIFT-COFB
Akiko Inoue, Chun Guo, and Kazuhiko Minematsu
We analyze nonce-misuse resilience (NMRL) security of Romulus-N and GIFT-COFB, the two finalists of NIST Lightweight Cryptography project for standardizing lightweight authenticated encryption. NMRL, introduced by Ashur et al. at CRYPTO 2017, is a relaxed security notion from a stronger, nonce-misuse resistance notion. We proved that Romulus-N and GIFT-COFB have nonce-misuse resilience. For Romulus-N, we showed the perfect privacy (NMRL-PRIV) and n/2-bit authenticity (NMRL-AUTH) with graceful degradation with respect to nonce repetition. For GIFT-COFB, we showed n/4-bit security for both NMRL-PRIV and NMRL-AUTH notions.
Last updated:  2022-08-05
A Fast, Practical and Simple Shortest Path Protocol for Multiparty Computation
Abdelrahaman Aly and Sara Cleemput
We present a simple and fast protocol to securely solve the (single source) Shortest Path Problem, based on Dijkstra's algorithm over Secure Multiparty Computation. Our protocol improves current state of the art by Aly et al. [FC 2013 & ICISC 2014] and can offer perfect security against both semi-honest and malicious adversaries. Furthermore, it is the first data oblivious protocol to achieve quadratic complexity in the number of communication rounds. Moreover, our protocol can be easily be adapted to form a subroutine in other combinatorial mechanisms. Our focus is usability; hence, we provide an open source implementation and exhaustive benchmarking under different adversarial settings and players setups.
Last updated:  2022-08-05
Spatial Encryption Revisited: From Delegatable Multiple Inner Product Encryption and More
Huy Quoc Le, Dung Hoang Duong, Willy Susilo, and Josef Pieprzyk
Spatial Encryption (SE), which involves encryption and decryption with affne/vector objects, was introduced by Boneh and Hamburg at Asiacrypt 2008. Since its introduction, SE has been shown as a versatile and elegant tool for implementing many other important primitives such as (Hierarchical) Identity-based Encryption ((H)IBE), Broadcast (H)IBE, Attribute-based Encryption, and Forward-secure cryptosystems. This paper revisits SE toward a more compact construction in the lattice setting. In doing that, we introduce a novel primitive called Delegatable Multiple Inner Product Encryption (DMIPE). It is a delegatable generalization of Inner Product Encryption (IPE) but different from the Hierarchical IPE (HIPE) (Okamoto and Takashima at Asiacrypt 2009). We point out that DMIPE and SE are equivalent in the sense that there are security-preserving conversions between them. As a proof of concept, we then successfully instantiate a concrete DMIPE construction relying on the hardness of the decisional learning with errors problem. In turn, the DMIPE design implies a more compact lattice-based SE in terms of sizes compared with SEs converted from HIPE (e.g., Xagawa’s HIPE at PKC 2013) using the framework by Chen et al. (Designs, Codes, and Cryptography, 2014). Furthermore, we demonstrate that one can also use SE to implement the Allow-/Deny-list encryption, which subsumes, e.g., puncturable encryption (Green and Miers at IEEE S&P 2015).
Last updated:  2022-08-05
Structure-Aware Private Set Intersection, With Applications to Fuzzy Matching
Gayathri Garimella, Mike Rosulek, and Jaspal Singh
In two-party private set intersection (PSI), Alice holds a set $X$, Bob holds a set $Y$, and they learn (only) the contents of $X \cap Y$. We introduce structure-aware PSI protocols, which take advantage of situations where Alice's set $X$ is publicly known to have a certain structure. The goal of structure-aware PSI is to have communication that scales with the description size of Alice's set, rather its cardinality. We introduce a new generic paradigm for structure-aware PSI based on function secret-sharing (FSS). In short, if there exists compact FSS for a class of structured sets, then there exists a semi-honest PSI protocol that supports this class of input sets, with communication cost proportional only to the FSS share size. Several prior protocols for efficient (plain) PSI can be viewed as special cases of our new paradigm, with an implicit FSS for unstructured sets. Our PSI protocol can be instantiated from a significantly weaker flavor of FSS, which has not been previously studied. We develop several improved FSS techniques that take advantage of these relaxed requirements, and which are in some cases exponentially better than existing FSS. Finally, we explore in depth a natural application of structure-aware PSI. If Alice's set $X$ is the union of many radius-$\delta$ balls in some metric space, then an intersection between $X$ and $Y$ corresponds to fuzzy PSI, in which the parties learn which of their points are within distance $\delta$. In structure-aware PSI, the communication cost scales with the number of balls in Alice's set, rather than their total volume. Our techniques lead to efficient fuzzy PSI for $\ell_\infty$ and $\ell_1$ metrics (and approximations of $\ell_2$ metric) in high dimensions. We implemented this fuzzy PSI protocol for 2-dimensional $\ell_\infty$ metrics. For reasonable input sizes, our protocol requires 45--60% less time and 85% less communication than competing approaches that simply reduce the problem to plain PSI.
Last updated:  2022-08-05
Time-Space Tradeoffs for Sponge Hashing: Attacks and Limitations for Short Collisions
Cody Freitag, Ashrujit Ghoshal, and Ilan Komargodski
Sponge hashing is a novel alternative to the popular Merkle-Damgård hashing design. The sponge construction has become increasingly popular in various applications, perhaps most notably, it underlies the SHA-3 hashing standard. Sponge hashing is parametrized by two numbers, $r$ and $c$ (bitrate and capacity, respectively), and by a fixed-size permutation on $r+c$ bits. In this work, we study the collision resistance of sponge hashing instantiated with a random permutation by adversaries with arbitrary $S$-bit auxiliary advice input about the random permutation that make $T$ online queries. Recent work by Coretti et al. (CRYPTO '18) showed that such adversaries can find collisions (with respect to a random $c$-bit initialization vector) with advantage $\Theta(ST^2/2^c + T^2/ 2^{r})$. Although the above attack formally breaks collision resistance in some range of parameters, its practical relevance is limited since the resulting collision is very long (on the order of $T$ blocks). Focusing on the task of finding short collisions, we study the complexity of finding a $B$-block collision for a given parameter $B\ge 1$. We give several new attacks and limitations. Most notably, we give a new attack that results in a single-block collision and has advantage $$ \Omega \left(\left(\frac{S^{2}T}{2^{2c}}\right)^{2/3} + \frac{T^2}{2^r}\right). $$ In certain range of parameters (e.g., $ST^2>2^c$), our attack outperforms the previously-known best attack. To the best of our knowledge, this is the first natural application for which sponge hashing is provably less secure than the corresponding instance of Merkle-Damgård hashing. Our attack relies on a novel connection between single-block collision finding in sponge hashing and the well-studied function inversion problem. We also give a general attack that works for any $B\ge 2$ and has advantage $\Omega({STB}/{2^{c}} + {T^2}/{2^{\min\{r,c\}}})$, adapting an idea of Akshima et al. (CRYPTO '20). We complement the above attacks with bounds on the best possible attacks. Specifically, we prove that there is a qualitative jump in the advantage of best possible attacks for finding unbounded-length collisions and those for finding very short collisions. Most notably, we prove (via a highly non-trivial compression argument) that the above attack is optimal for $B=2$ in some range of parameters.
Last updated:  2022-08-05
Multimodal Private Signatures
Khoa Nguyen, Fuchun Guo, Willy Susilo, and Guomin Yang
We introduce Multimodal Private Signature (MPS) - an anonymous signature system that offers a novel accountability feature: it allows a designated opening authority to learn some partial information $\mathsf{op}$ about the signer's identity $\mathsf{id}$, and nothing beyond. Such partial information can flexibly be defined as $\mathsf{op} = \mathsf{id}$ (as in group signatures), or as $\mathsf{op} = \mathbf{0}$ (like in ring signatures), or more generally, as $\mathsf{op} = G_j(\mathsf{id})$, where $G_j(\cdot)$ is a certain disclosing function. Importantly, the value of $\mathsf{op}$ is known in advance by the signer, and hence, the latter can decide whether she/he wants to disclose that piece of information. The concept of MPS significantly generalizes the notion of tracing in traditional anonymity-oriented signature primitives, and can enable various new and appealing privacy-preserving applications. We formalize the definitions and security requirements for MPS. We next present a generic construction to demonstrate the feasibility of designing MPS in a modular manner and from commonly used cryptographic building blocks (ordinary signatures, public-key encryption and NIZKs). We also provide an efficient construction in the standard model based on pairings, and a lattice-based construction in the random oracle model.
Last updated:  2022-08-05
zkQMC: Zero-Knowledge Proofs For (Some) Probabilistic Computations Using Quasi-Randomness
Zachary DeStefano, Dani Barrack, and Michael Dixon
We initiate research into efficiently embedding probabilistic computations in probabilistic proofs by introducing techniques for capturing Monte Carlo methods and Las Vegas algorithms in zero knowledge and exploring several potential applications of these techniques. We design and demonstrate a technique for proving the integrity of certain randomized computations, such as uncertainty quantification methods, in non-interactive zero knowledge (NIZK) by replacing conventional randomness with low-discrepancy sequences. This technique, known as the Quasi-Monte Carlo (QMC) method, functions as a form of weak algorithmic derandomization to efficiently produce adversarial-resistant worst-case uncertainty bounds for the results of Monte Carlo simulations. The adversarial resistance provided by this approach allows the integrity of results to be verifiable both in interactive and non-interactive zero knowledge without the need for additional statistical or cryptographic assumptions. To test these techniques, we design a custom domain specific language and implement an associated compiler toolchain that builds zkSNARK gadgets for expressing QMC methods. We demonstrate the power of this technique by using this framework to benchmark zkSNARKs for various examples in statistics and physics. Using $N$ samples, our framework produces zkSNARKs for numerical integration problems of dimension $d$ with $O\left(\frac{(\log N)^d}{N}\right)$ worst-case error bounds. Additionally, we prove a new result using discrepancy theory to efficiently and soundly estimate the output of computations with uncertain data with an $O\left(d\frac{\log N}{\sqrt[d]{N}}\right)$ worst-case error bound. Finally, we show how this work can be applied more generally to allow zero-knowledge proofs to capture a subset of decision problems in $\mathsf{BPP}$, $\mathsf{RP}$, and $\mathsf{ZPP}$.
Last updated:  2022-08-04
A Forward-secure Efficient Two-factor Authentication Protocol
Steven J. Murdoch and Aydin Abadi
Two-factor authentication(2FA)schemes that rely on a combination of knowledge factors (e.g., PIN) and device possession have gained popularity. Some of these schemes remain secure even against strong adversaries that (a) observe the traffic between a client and server, and (b) have physical access to the client’s device, or its PIN, or breach the server. However, these solutions have several shortcomings; namely, they (i) require a client to remember multiple secret values to prove its identity, (ii) involve several modular exponentiations, and (iii) are in the non-standard random oracle model. In this work, we present a 2FA protocol that resists such a strong adversary while addressing the above shortcomings. Our protocol requires a client to remember only a single secret value/PIN, does not involve any modular exponentiations, and is in a standard model. It is the first one that offers these features without using trusted chipsets. This protocol also imposes up to 40% lower communication overhead than the state-of-the-art solutions do.
Last updated:  2022-08-04
PUF-COTE: A PUF Construction with Challenge Obfuscation and Throughput Enhancement
Boyapally Harishma, Durba Chatterjee, Kuheli Pratihar, Sayandeep Saha, and Debdeep Mukhopadhyay
Physically Unclonable Functions~(PUFs) have been a potent choice for enabling low-cost, secure communication. However, the state-of-the-art strong PUFs generate single-bit response. So, we propose PUF-COTE: a high throughput architecture based on linear feedback shift register and a strong PUF as the ``base''-PUF. At the same time, we obfuscate the challenges to the ``base''-PUF of the final construction. We experimentally evaluate the quality of the construction by implementing it on Artix 7 FPGAs. We evaluate the statistical quality of the responses~(using NIST SP800-92 test suit and standard PUF metrics: uniformity, uniqueness, reliability, strict avalanche criterion, ML-based modelling), which is a crucial factor for cryptographic applications.
Last updated:  2022-08-04
Interactive Non-Malleable Codes Against Desynchronizing Attacks in the Multi-Party Setting
Nils Fleischhacker, Suparno Ghoshal, and Mark Simkin
Interactive Non-Malleable Codes were introduced by Fleischhacker et al. (TCC 2019) in the two party setting with synchronous tampering. The idea of this type of non-malleable code is that it "encodes" an interactive protocol in such a way that, even if the messages are tampered with according to some class $\mathcal{F}$ of tampering functions, the result of the execution will either be correct, or completely unrelated to the inputs of the participating parties. In the synchronous setting the adversary is able to modify the messages being exchanged but cannot drop messages nor desynchronize the two parties by first running the protocol with the first party and then with the second party. In this work, we define interactive non-malleable codes in the non-synchronous multi-party setting and construct such interactive non-malleable codes for the class $\mathcal{F}^{s}_{\textsf{bounded}}$ of bounded-state tampering functions. The construction is applicable to any multi-party protocol with a fixed message topology.
Last updated:  2022-08-04
FairTraDEX: A Decentralised Exchange Preventing Value Extraction
Conor McMenamin, Vanesa Daza, Matthias Fitzi, and Padraic O'Donoghue
We present FairTraDEX, a decentralized exchange (DEX) protocol based on frequent batch auctions (FBAs), which provides formal game-theoretic guarantees against extractable value. FBAs when run by a trusted third-party provide unique game-theoretic optimal strategies which ensure players are shown prices equal to the liquidity provider's fair price, excluding explicit, pre-determined fees. FairTraDEX replicates the key features of an FBA that provide these game-theoretic guarantees using a combination of set-membership in zero-knowledge protocols and an escrow-enforced commit-reveal protocol. We extend the results of FBAs to handle monopolistic and/or malicious liquidity providers. We provide real-world examples that demonstrate that the costs of executing orders in existing academic and industry-standard protocols become prohibitive as order size increases due to basic value extraction techniques, popularized as maximal extractable value. We further demonstrate that FairTraDEX protects against these execution costs, guaranteeing a fixed fee model independent of order size, the first guarantee of it's kind for a DEX protocol. We also provide detailed Solidity and pseudo-code implementations of FairTraDEX, making FairTraDEX a novel and practical contribution.
Last updated:  2022-08-04
Orbis Specification Language: a type theory for zk-SNARK programming
Morgan Thomas
Orbis Specification Language (OSL) is a language for writing statements to be proven by zk-SNARKs. zk-SNARK theories allow for proving wide classes of statements. They usually require the statement to be proven to be expressed as a constraint system, called an arithmetic circuit, which can take various forms depending on the theory. It is difficult to express complex statements in the form of arithmetic circuits. OSL is a language of statements which is similar to type theories used in proof engineering, such as Agda and Coq. OSL has a feature set which is sufficiently limited to make it feasible to compile a statement expressed in OSL to an arithmetic circuit which expresses the same statement. This work builds on Σ1 arithmetization [5] in Halo 2 [3, 4], by defining a frontend for a user-friendly circuit compiler.
Last updated:  2022-08-04
Zswap: zk-SNARK Based Non-Interactive Multi-Asset Swaps
Felix Engelmann, Thomas Kerber, Markulf Kohlweiss, and Mikhail Volkhov
Privacy-oriented cryptocurrencies, like Zcash or Monero, provide fair transaction anonymity and confidentiality but lack important features compared to fully public systems, like Ethereum. Specifically, supporting assets of multiple types and providing a mechanism to atomically exchange them, which is critical for e.g. decentralized finance (DeFi), is challenging in the private setting. By combining insights and security properties from Zcash and SwapCT (PETS 21, an atomic swap system for Monero), we present a simple zk-SNARKs-based transaction scheme, called Zswap, which is carefully malleable to allow the merging of transactions, while preserving anonymity. Our protocol enables multiple assets and atomic exchanges by making use of sparse homomorphic commitments with aggregated open randomness, together with Zcash-friendly simulation-extractable non-interactive zero-knowledge (NIZK) proofs. This results in a provably secure privacy-preserving transaction protocol, with efficient swaps, and overall performance close to that of existing deployed private cryptocurrencies. It is similar to Zcash Sapling and benefits from existing code bases and implementation expertise.
Last updated:  2022-08-04
Quantum Security of FOX Construction based on Lai-Massey Scheme
Amit Kumar Chauhan and Somitra Sanadhya
The Lai-Massey scheme is an important cryptographic approach to design block ciphers from secure pseudorandom functions. It has been used in the designs of IDEA and IDEA-NXT. At ASIACRYPT'99, Vaudenay showed that the 3-round and 4-round Lai-Massey scheme are secure against chosen-plaintext attacks (CPAs) and chosen-ciphertext attacks (CCAs), respectively, in the classical setting. At SAC'04, Junod and Vaudenay proposed a new family of block ciphers based on the Lai-Massey scheme, namely FOX. In this work, we analyze the security of the FOX cipher in the quantum setting, where the attacker can make quantum superposed queries to the oracle. Our results are as follows: $-$ The 3-round FOX construction is not a pseudorandom permutation against quantum chosen-plaintext attacks (qCPAs), and the 4-round FOX construction is not a strong pseudorandom permutation against quantum chosen-ciphertext attacks (qCCAs). Essentially, we build quantum distinguishers against the 3-round and 4-round FOX constructions, using Simon's algorithm. $-$ The 4-round FOX construction is a pseudorandom permutation against qCPAs. Concretely, we prove that the 4-round FOX construction is secure up to $O(2^{n/12})$ quantum queries. Our security proofs use the compressed oracle technique introduced by Zhandry. More precisely, we use an alternative formalization of the compressed oracle technique introduced by Hosoyamada and Iwata.
Last updated:  2022-08-04
Lattice Codes for Lattice-Based PKE
Shanxiang Lyu, Ling Liu, Junzuo Lai, Cong Ling, and Hao Chen
The public key encryption (PKE) protocol in lattice-based cryptography (LBC) can be modeled as a noisy point-to-point communication system, where the communication channel is similar to the additive white Gaussian noise (AWGN) channel. To improve the error correction performance, this paper investigates lattice-based PKE from the perspective of lattice codes. We propose an efficient labeling function that converts between binary information bits and lattice codewords. The proposed labeling is feasible for a wide range of lattices, including Construction-A and Construction-D lattices. Based on Barnes-Wall lattices, a few improved parameter sets with either higher security or smaller ciphertext size are proposed for FrodoPKE.
Last updated:  2022-08-03
Piranha: A GPU Platform for Secure Computation
Jean-Luc Watson, Sameer Wagh, and Raluca Ada Popa
Secure multi-party computation (MPC) is an essential tool for privacy-preserving machine learning (ML). However, secure training of large-scale ML models currently requires a prohibitively long time to complete. Given that large ML inference and training tasks in the plaintext setting are significantly accelerated by Graphical Processing Units (GPUs), this raises the natural question: can secure MPC leverage GPU acceleration? A few recent works have studied this question in the context of accelerating specific components or protocols, but do not provide a general-purpose solution. Consequently, MPC developers must be both experts in cryptographic protocol design and proficient at low-level GPU kernel development to achieve good performance on any new protocol implementation. We present Piranha, a general-purpose, modular platform for accelerating secret sharing-based MPC protocols using GPUs. Piranha allows the MPC community to easily leverage the benefits of a GPU without requiring GPU expertise. Piranha contributes a three-layer architecture: (1) a device layer that can independently accelerate secret-sharing protocols by providing integer-based kernels absent in current general-purpose GPU libraries, (2) a modular protocol layer that allows developers to maximize utility of limited GPU memory with in-place computation and iterator-based support for non-standard memory access patterns, and (3) an application layer that allows applications to remain completely agnostic to the underlying protocols they use. To demonstrate the benefits of Piranha, we implement 3 state-of-the-art linear secret sharing MPC protocols for secure NN training: 2-party SecureML (IEEE S&P ’17), 3-party Falcon (PETS ’21), and 4-party FantasticFour (USENIX Security ’21). Compared to their CPU-based implementations, the same protocols implemented on top of Piranha’s protocol-agnostic acceleration exhibit a 16−48× decrease in training time. For the first time, Piranha demonstrates the feasibility of training a realistic neural network (e.g. VGG), end-to-end, using MPC in a little over one day. Piranha is open source and available at
Last updated:  2022-08-03
How to Prove Schnorr Assuming Schnorr: Security of Multi- and Threshold Signatures
Elizabeth Crites, Chelsea Komlo, and Mary Maller
This work investigates efficient multi-party signature schemes in the discrete logarithm setting. We focus on a concurrent model, in which an arbitrary number of signing sessions may occur in parallel. Our primary contributions are: (1) a modular framework for proving the security of Schnorr multisignature and threshold signature schemes, (2) an optimization of the two-round threshold signature scheme $\mathsf{FROST}$ that we call $\mathsf{FROST2}$, and (3) the application of our framework to prove the security of $\mathsf{FROST2}$ as well as a range of other multi-party schemes. We begin by demonstrating that our framework is applicable to multisignatures. We prove the security of a variant of the two-round $\mathsf{MuSig2}$ scheme with proofs of possession and a three-round multisignature $\mathsf{SimpleMuSig}$. We introduce a novel three-round threshold signature $\mathsf{SimpleTSig}$ and propose an optimization to the two-round $\mathsf{FROST}$ threshold scheme that we call $\mathsf{FROST2}$. $\mathsf{FROST2}$ reduces the number of scalar multiplications required during signing from linear in the number of signers to constant. We apply our framework to prove the security of $\mathsf{FROST2}$ under the one-more discrete logarithm assumption and $\mathsf{SimpleTSig}$ under the discrete logarithm assumption in the programmable random oracle model.
Last updated:  2022-08-03
Statistical Decoding 2.0: Reducing Decoding to LPN
Kevin Carrier, Thomas Debris-Alazard, Charles Meyer-Hilfiger, and Jean-Pierre Tillich
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information set decoders (ISD). A while ago, a generic decoding algorithm which does not belong to this family was proposed: statistical decoding. It is a randomized algorithm that requires the computation of a large set of parity-checks of moderate weight, and uses some kind of majority voting on these equations to recover the error. This algorithm was long forgotten because even the best variants of it performed poorly when compared to the simplest ISD algorithm. We revisit this old algorithm by using parity-check equations in a more general way. Here the parity-checks are used to get LPN samples with a secret which is part of the error and the LPN noise is related to the weight of the parity-checks we produce. The corresponding LPN problem is then solved by standard Fourier techniques. By properly choosing the method of producing these low weight equations and the size of the LPN problem, we are able to outperform in this way significantly information set decodings at code rates smaller than $0.3$. It gives for the first time after $60$ years, a better decoding algorithm for a significant range which does not belong to the ISD family.
Last updated:  2022-08-03
An $\mathcal{O}(n)$ Algorithm for Coefficient Grouping
Fukang Liu
In this note, we study a specific optimization problem arising in the recently proposed coefficient grouping technique, which is used for the degree evaluation. Specifically, we show that there exists an efficient algorithm running in time $\mathcal{O}(n)$ to solve a basic optimization problem relevant to upper bound the algebraic degree. We expect that some results in this note can inspire more studies on other optimization problems in the coefficient grouping technique.
Last updated:  2022-08-03
PipeMSM: Hardware Acceleration for Multi-Scalar Multiplication
Charles. F. Xavier
Multi-Scalar Multiplication (MSM) is a fundamental computational problem. Interest in this problem was recently prompted by its application to ZK-SNARKs, where it often turns out to be the main computational bottleneck. In this paper we set forth a pipelined design for computing MSM. Our design is based on a novel algorithmic approach and hardware-specific optimizations. At the core, we rely on a modular multiplication technique which we deem to be of independent interest. We implemented and tested our design on FPGA. We highlight the promise of optimized hardware over state-of-the-art GPU- based MSM solver in terms of speed and energy expenditure.
Last updated:  2022-08-03
Quantum-Resistant Password-Based Threshold Single-Sign-On Authentication with Updatable Server Private Key
Jingwei Jiang, Ding Wang, Guoyin Zhang, and Zhiyuan Chen
Passwords are the most prevalent authentication mechanism and proliferate on nearly every new web service. As users are overloaded with the tasks of managing dozens even hundreds of passwords, accordingly password-based single-sign-on (SSO) schemes have been proposed. In password-based SSO schemes, the authentication server needs to maintain a sensitive password file, which is an attractive target for compromise and poses a single point of failure. Hence, the notion of password-based threshold authentication (PTA) system has been proposed. However, a static PTA system is threatened by perpetual leakage (e.g., the adversary perpetually compromises servers). In addition, most of the existing PTA schemes are built on the intractability of conventional hard problems and become insecure in the quantum era. In this work, we first propose a threshold oblivious pseudorandom function (TOPRF) to harden the password so that PTA schemes can resist offline password guessing attacks. Then, we employ the threshold homomorphic aggregate signature (THAS) over lattices to construct the first quantum-resistant password-based threshold single-sign-on authentication scheme with the updatable server private key. Our scheme resolves various issues arising from user corruption and server compromise, and it is formally proved secure against quantum adversaries. Comparison results show that our scheme is superior to its counterparts.
Last updated:  2022-08-03
On the Hardness of the Finite Field Isomorphism Problem
Dipayan Das and Antoine Joux
The finite field isomorphism FFI problem, introduced in PKC'18, is an alternative to average-case lattice problems (like LWE, SIS, or NTRU). As an application, the FFI problem is used to construct a fully homomorphic encryption scheme in the same paper. In this work, we prove that the decision variant of the FFI problem can be solved in polynomial time for any field characteristics $q= \Omega(\beta n^2)$, where $q,\beta,n$ parametrize the FFI problem. Then we use our result from the FFI distinguisher to propose a polynomial-time attack on the semantic security of the fully homomorphic encryption scheme. Furthermore, for completeness, we also study the search variant of the FFI problem and show how to state it as a $q$-ary lattice problem, which was previously unknown. As a result, we can solve the search problem for some previously intractable parameters using a simple lattice reduction approach.
Last updated:  2022-08-03
Key-Recovery Attacks on CRAFT and WARP (Full Version)
Ling Sun, Wei Wang, and Meiqin Wang
This paper considers the security of CRAFT and WARP. We present a practical key-recovery attack on full-round CRAFT in the related-key setting with only one differential characteristic, and the theoretical time complexity of the attack is $2^{36.09}$ full-round encryptions. The attack is verified in practice. The test result indicates that the theoretical analysis is valid, and it takes about $15.69$ hours to retrieve the key. A full-round key-recovery attack on WARP in the related-key setting is proposed, and the time complexity is $2^{44.58}$ full-round encryptions. The theoretical attack is implemented on a round-reduced version of WARP, which guarantees validity. Besides, we give a 33-round multiple zero-correlation linear attack on WARP, which is the longest attack on the cipher in the single-key attack setting. We note that the attack results in this paper do not threaten the security of CRAFT and WARP as the designers do not claim security under the related-key attack setting.
Last updated:  2022-08-03
Fast Hashing to $G_2$ in Direct Anonymous Attestation
Yu Dai, Fangguo Zhang, and Chang-An Zhao
To reduce the workload of the Trusted Platform Module~(TPM) without affecting the security in pairing-based direct anonymous attestation~(DAA) schemes, it is feasible to select pairing-friendly curves that provide fast group operations in the first pairing subgroup. In this scenario, the BW13-P310 and BW19-P286 curves become competitive. In order to improve the efficiency of the DAA schemes based on these curves, it is also necessary to design an efficient algorithm for hashing to $G_2$. In this paper, we first generalize the previous work to address the bottlenecks involved in hashing to $G_2$ on the two curves. On this basis, we further optimize the hashing algorithm, which would be nearly twice as fast as the previous one in theory. These techniques actually can be applied to a large class of curves. We also implement the proposed algorithms over the BW13-P310 curve on a 64-bit computing platform.
Last updated:  2022-08-03
Secure Joint Communication and Sensing
Onur Gunlu, Matthieu Bloch, Rafael F. Schaefer, and Aylin Yener
This work considers mitigation of information leakage between communication and sensing operations in joint communication and sensing systems. Specifically, a discrete memoryless state-dependent broadcast channel model is studied in which (i) the presence of feedback enables a transmitter to simultaneously achieve reliable communication and channel state estimation; (ii) one of the receivers is treated as an eavesdropper whose state should be estimated but which should remain oblivious to a part of the transmitted information. The model abstracts the challenges behind security for joint communication and sensing if one views the channel state as a characteristic of the receiver, e.g., its location. For independent and identically distributed (i.i.d.) states, perfect output feedback, and when part of the transmitted message should be kept secret, a partial characterization of the secrecy-distortion region is developed. The partial characterization is simplified when the broadcast channel is either physically-degraded or reversely-physically-degraded. The characterization is also extended to the situation in which the entire transmitted message should be kept secret, for which the characterization is exact for physically-degraded and reversely-physically-degraded channels. The benefits of a joint approach compared to separation-based secure communication and state-sensing methods are illustrated with a binary joint communication and sensing model.
Last updated:  2022-08-03
Opportunistic Algorithmic Double-Spending: How I learned to stop worrying and hedge the Fork
Nicholas Stifter, Aljosha Judmayer, Philipp Schindler, and Edgar Weippl
In this paper, we outline a novel form of attack we refer to as Opportunistic Algorithmic Double-Spending (OpAl ). OpAl attacks avoid equivocation, i.e., do not require conflicting transactions, and are carried out automatically in case of a fork. Algorithmic double-spending is facilitated through transaction semantics that dynamically depend on the context and ledger state at the time of execution. Hence, OpAl evades common double-spending detection mechanisms and can opportunistically leverage forks, even if the malicious sender themselves is not responsible for, or even actively aware of, any fork. Forkable ledger designs with expressive transaction semantics, especially stateful EVM-based smart contract platforms such as Ethereum, are particularly vulnerable. Hereby, the cost of modifying a regular transaction to opportunistically perform an OpAl attack is low enough to consider it a viable default strategy. While Bitcoin’s stateless UTXO model, or Cardano’s EUTXO model, appear more robust against OpAl , we nevertheless demonstrate scenarios where transactions are semantically malleable and thus vulnerable. To determine whether OpAl -like semantics can be observed in practice, we analyze the execution traces of 922562 transactions on the Ethereum blockchain. Hereby, we are able to identify transactions, which may be associated with frontrunning and MEV bots, that exhibit some of the design patterns also employed as part of the herein presented attack.
Last updated:  2022-08-03
Faster Sounder Succinct Arguments and IOPs
Justin Holmgren and Ron Rothblum
Succinct arguments allow a prover to convince a verifier that a given statement is true, using an extremely short proof. A major bottleneck that has been the focus of a large body of work is in reducing the overhead incurred by the prover in order to prove correctness of the computation. By overhead we refer to the cost of proving correctness, divided by the cost of the original computation. In this work, for a large class of Boolean circuits $C=C(x,w)$, we construct succinct arguments for the language $\{ x : \exists w\; C(x,w)=1\}$, with $2^{-\lambda}$ soundness error, and with prover overhead $\mathsf{polylog}(\lambda)$. This result relies on the existence of (sub-exponentially secure) linear-size computable collision-resistant hash functions. The class of Boolean circuits that we can handle includes circuits with a repeated sub-structure, which arise in natural applications such as batch computation/verification, hashing and related block chain applications. The succinct argument is obtained by constructing \emph{interactive oracle proofs} for the same class of languages, with $\mathsf{polylog}(\lambda)$ prover overhead, and soundness error $2^{-\lambda}$. Prior to our work, the best IOPs for Boolean circuits either had prover overhead of $\mathsf{polylog}(|C|)$ based on efficient PCPs due to Ben-Sasson et al. (STOC, 2013) or $\mathsf{poly}(\lambda)$ due to Rothblum and Ron-Zewi (STOC, 2022).
Last updated:  2022-08-03
A New Look at Blockchain Leader Election: Simple, Efficient, Sustainable and Post-Quantum
Muhammed F. Esgin, Oguzhan Ersoy, Veronika Kuchta, Julian Loss, Amin Sakzad, Ron Steinfeld, Wayne Yang, and Raymond K. Zhao
In this work, we study the blockchain leader election problem. The purpose of such protocols is to elect a leader who decides on the next block to be appended to the blockchain, for each block proposal round. Solutions to this problem are vital for the security of blockchain systems. We introduce an efficient blockchain leader election method with security based solely on standard assumptions for cryptographic hash functions (rather than public-key cryptographic assumptions) and that does not involve a racing condition as in Proof-of-Work based approaches. Thanks to the former feature, our solution provides the highest confidence in security, even in the post-quantum era. A particularly scalable application of our solution is in the Proof-of-Stake setting, and we investigate our solution in the Algorand blockchain system. We believe our leader election approach can be easily adapted to a range of other blockchain settings. At the core of Algorand's leader election is a verifiable random function (VRF). Our approach is based on introducing a simpler primitive which still suffices for the blockchain leader election problem. In particular, we analyze the concrete requirements in an Algorand-like blockchain setting to accomplish leader election, which leads to the introduction of indexed VRF (iVRF). An iVRF satisfies modified uniqueness and pseudorandomness properties (versus a full-fledged VRF) that enable an efficient instantiation based on a hash function without requiring any complicated zero-knowledge proofs of correct PRF evaluation. We further extend iVRF to an authenticated iVRF with forward-security, which meets all the requirements to establish an Algorand-like consensus. Our solution is simple, flexible and incurs only a 32-byte additional overhead when combined with the current best solution to constructing a forward-secure signature (in the post-quantum setting). We implemented our (authenticated) iVRF proposal in C language on a standard computer and show that our proposal significantly outperforms other quantum-safe VRF proposals in almost all metrics. Particularly, iVRF evaluation and verification can be executed in 0.02 ms, which is even faster than ECVRF used in Algorand.
Last updated:  2022-08-02
Sequential Digital Signatures for Cryptographic Software-Update Authentication
Bertram Poettering and Simon Rastikian
Consider a computer user who needs to update a piece of software installed on their computing device. To do so securely, a commonly accepted ad-hoc method stipulates that the old software version first retrieves the update information from the vendor's public repository, then checks that a cryptographic signature embedded into it verifies with the vendor's public key, and finally replaces itself with the new version. This updating method seems to be robust and lightweight, and to reliably ensure that no malicious third party (e.g., a distribution mirror) can inject harmful code into the update process. Unfortunately, recent prominent news reports (SolarWinds, Stuxnet, TikTok, Zoom, ...) suggest that nation state adversaries are broadening their efforts related to attacking software supply chains. This calls for a critical re-evaluation of the described signature based updating method with respect to the real-world security it provides against particularly powerful adversaries. We approach the setting by formalizing a cryptographic primitive that addresses specifically the secure software updating problem. We define strong, rigorous security models that capture forward security (stealing a vendor's key today doesn't allow modifying yesterday's software version) as well as a form of self-enforcement that helps protecting vendors against coercion attacks in which they are forced, e.g. by nation state actors, to misuse or disclose their keys. We note that the common signature based software authentication method described above meets neither the one nor the other goal, and thus represents a suboptimal solution. Hence, after formalizing the syntax and security of the new primitive, we propose novel, efficient, and provably secure constructions.
Last updated:  2022-08-02
A toolbox for verifiable tally-hiding e-voting systems
Véronique Cortier, Pierrick Gaudry, and Quentin Yang
In most verifiable electronic voting schemes, one key step is the tally phase, where the election result is computed from the encrypted ballots. A generic technique consists in first applying (verifiable) mixnets to the ballots and then revealing all the votes in the clear. This however discloses much more information than the result of the election itself (that is, the winners) and may offer the possibility to coerce voters. In this paper, we present a collection of building blocks for designing tally-hiding schemes based on multi-party computations. As an application, we propose the first efficient tally-hiding schemes with no leakage for four important counting functions: D'Hondt, Condorcet, STV, and Majority Judgment. We prove that they can be used to design a private and verifiable voting scheme. We also unveil unknown flaws or leakage in several previously proposed tally-hiding schemes.
Last updated:  2022-08-02
Quantum Implementation and Analysis of DEFAULT
Kyungbae Jang, Anubhab Baksi, Jakub Breier, Hwajeong Seo, and Anupam Chattopadhyay
In this paper, we present the quantum implementation and analysis of the recently proposed block cipher, DEFAULT. DEFAULT is consisted of two components, namely DEFAULT-LAYER and DEFAULT-CORE. Two instances of DEFAULT-LAYER is used before and after DEFAULT-CORE (the so-called `sandwich construction'). We discuss about the the various choices made to keep the cost for the basic quantum circuit and that of the Grover's oracle search, and compare it with the levels of quantum security specified by the United States' National Institute of Standards and Technology (NIST). All in all, our work nicely fits in the research trend of finding the possible quantum vulnerability of symmetric key ciphers.
Last updated:  2022-08-02
He-HTLC: Revisiting Incentives in HTLC
Sarisht Wadhwa, Jannis Stoeter, Fan Zhang, and Kartik Nayak
Hashed Time-Locked Contracts (HTLCs) are a widely used primitive in blockchain systems such as payment channels, atomic swaps, etc. Unfortunately, HTLC is incentive-incompatible and is vulnerable to bribery attacks. The state-of-the-art solution is MAD-HTLC (Oakland'21), which proposes an elegant idea that leverages miners' profit-driven nature to defeat bribery attacks. In this paper, we show that MAD-HTLC is still vulnerable as it only considers a somewhat narrow set of passive strategies by miners. Through a family of novel reverse-bribery attacks, we show concrete active strategies that miners can take to break MAD-HTLC and profit at the loss of MAD-HTLC users. For these attacks, we present their implementation and game-theoretical profitability analysis. Based on the learnings from our attacks, we propose a new HTLC realization, He-HTLC (Our specification is lightweight and inert to incentive manipulation attacks. Hence, we call it He-HTLC where He stands for Helium.) that is provably secure against all possible strategic manipulation (passive and active). In addition to being secure in a stronger adversary model, He-HTLC achieves other desirable features such as low and user-adjustable collateral, making it more practical to implement and use the proposed schemes. We implemented He-HTLC on Bitcoin and the transaction cost of He-HTLC is comparative to average Bitcoin transaction fees.
Last updated:  2022-08-02
Efficient Computation of (2^n,2^n)-Isogenies
Sabrina Kunzweiler
Elliptic curves are abelian varieties of dimension one; the two-dimensional analogue are abelian surfaces. In this work we present an algorithm to compute $(2^n,2^n)$-isogenies of abelian surfaces defined over finite fields. These isogenies are the natural generalization of $2^n$-isogenies of elliptic curves. Our algorithm is designed to be used in higher-dimensional variants of isogeny-based cryptographic protocols such as G2SIDH which is a genus-$2$ version of the Supersingular Isogeny Diffie-Hellman (SIDH) key exchange. We analyze the performance of our algorithm in cryptographically relevant settings and show that it significantly improves upon previous implementations. Different results deduced in the development of our algorithm are also interesting beyond this application. For instance, we derive a formula for the evaluation of $(2,2)$-isogenies. Given an element in Mumford coordinates, this formula outputs the (unreduced) Mumford coordinates of its image under the $(2,2)$-isogeny. Furthermore, we study $4$-torsion points on Jacobians of hyperelliptic curves and explain how to extract square-roots of coefficients of $2$-torsion points from these points.
Last updated:  2022-08-02
Modeling and Simulating the Sample Complexity of solving LWE using BKW-Style Algorithms
Qian Guo, Erik Mårtensson, and Paul Stankovski Wagner
The Learning with Errors (LWE) problem receives much attention in cryptography, mainly due to its fundamental significance in post-quantum cryptography. Among its solving algorithms, the Blum-Kalai-Wasserman (BKW) algorithm, originally proposed for solving the Learning Parity with Noise (LPN) problem, performs well, especially for certain parameter settings with cryptographic importance. The BKW algorithm consists of two phases, the reduction phase and the solving phase. In this work, we study the performance of distinguishers used in the solving phase. We show that the Fast Fourier Transform (FFT) distinguisher from Eurocrypt’15 has the same sample complexity as the optimal distinguisher, when making the same number of hypotheses. We also show via simulation that it performs much better than previous theory predicts and develop a sample complexity model that matches the simulations better. We also introduce an improved, pruned version of the FFT distinguisher. Finally, we indicate, via extensive experiments, that the sample dependency due to both LF2 and sample amplification is limited.
Last updated:  2022-08-02
A Signature-Based Gröbner Basis Algorithm with Tail-Reduced Reductors (M5GB)
Manuel Hauke, Lukas Lamster, Reinhard Lüftenegger, and Christian Rechberger
Gröbner bases are an important tool in computational algebra and, especially in cryptography, often serve as a boilerplate for solving systems of polynomial equations. Research regarding (efficient) algorithms for computing Gröbner bases spans a large body of dedicated work that stretches over the last six decades. The pioneering work of Bruno Buchberger in 1965 can be considered as the blueprint for all subsequent Gröbner basis algorithms to date. Among the most efficient algorithms in this line of work are signature-based Gröbner basis algorithms, with the first of its kind published in the late 1990s by Jean-Charles Faugère under the name $\texttt{F5}$. In addition to signature-based approaches, Rusydi Makarim and Marc Stevens investigated a different direction to efficiently compute Gröbner bases, which they published in 2017 with their algorithm $\texttt{M4GB}$. The ideas behind $\texttt{M4GB}$ and signature-based approaches are conceptually orthogonal to each other because each approach addresses a different source of inefficiency in Buchberger's initial algorithm by different means. We amalgamate those orthogonal ideas and devise a new Gröbner basis algorithm, called $\texttt{M5GB}$, that combines the concepts of both worlds. In that capacity, $\texttt{M5GB}$ merges strong signature-criteria to eliminate redundant S-pairs with concepts for fast polynomial reductions borrowed from $\texttt{M4GB}$. We provide proofs of termination and correctness and a proof-of-concept implementation in C++ by means of the Mathic library. The comparison with a state-of-the-art signature-based Gröbner basis algorithm (implemented via the same library) validates our expectations of an overall faster runtime for quadratic overdefined polynomial systems that have been used in comparisons before in the literature and are also part of cryptanalytic challenges.
Last updated:  2022-08-02
Quantum Attacks on Lai-Massey Structure
Shuping Mao, Tingting Guo, Peng Wang, and Lei Hu
Aaram Yun et al. considered that Lai-Massey structure has the same security as Feistel structure. However, Luo et al. showed that 3-round Lai-Massey structure can resist quantum attacks of Simon's algorithm, which is different from Feistel structure. We give quantum attacks against a typical Lai-Massey structure. The result shows that there exists a quantum CPA distinguisher against 3-round Lai-Massey structure and a quantum CCA distinguisher against 4-round Lai-Massey Structure, which is the same as Feistel structure. We extend the attack on Lai-Massey structure to quasi-Feistel structure. We show that if the combiner of quasi-Feistel structure is linear, there exists a quantum CPA distinguisher against 3-round balanced quasi-Feistel structure and a quantum CCA distinguisher against 4-round balanced quasi-Feistel Structure.
Last updated:  2022-08-02
Privacy when Everyone is Watching: An SOK on Anonymity on the Blockchain
Roy Rinberg and Nilaksh Agarwal
Blockchain technologies rely on a public ledger, where typically all transactions are pseudoanonymous and fully traceable. This poses a major flaw in its large scale adoption of cryptocurrencies, the primary application of blockchain technologies, as most individuals do not want to disclose their finances to the pub- lic. Motivated by the explosive growth in private-Blockchain research, this Statement-of-Knowledge (SOK) explores the ways to obtain privacy in this public ledger ecosystem. The authors first look at the underly- ing technology underling all zero-knowledge applications on the blockchain: zk-SNARKs (zero-knowledge Succinct Non-interactive ARguments of Knowledge). We then explore the two largest privacy coins as of today, ZCash and Monero, as well as TornadoCash, a popular Ethereum Tumbler solution. Finally, we look at the opposing incentives behind privacy solutions and de-anonymization techniques, and the future of privacy on the blockchain.
Last updated:  2022-08-01
ToSHI - Towards Secure Heterogeneous Integration: Security Risks, Threat Assessment, and Assurance
Nidish Vashistha, Md Latifur Rahman, Md Saad Ul Haque, Azim Uddin, Md Sami Ul Islam Sami, Amit Mazumder Shuo, Paul Calzada, Farimah Farahmandi, Navid Asadizanjani, Fahim Rahman, and Mark Tehranipoor
The semiconductor industry is entering a new age in which device scaling and cost reduction will no longer follow the decades-long pattern. Packing more transistors on a monolithic IC at each node becomes more difficult and expensive. Companies in the semiconductor industry are increasingly seeking technological solutions to close the gap and enhance cost-performance while providing more functionality through integration. Putting all of the operations on a single chip (known as a system on a chip, or SoC) presents several issues, including increased prices and greater design complexity. Heterogeneous integration (HI), which uses advanced packaging technology to merge components that might be designed and manufactured independently using the best process technology, is an attractive alternative. However, although the industry is motivated to move towards HI, many design and security challenges must be addressed. This paper presents a three-tier security approach for secure heterogeneous integration by investigating supply chain security risks, threats, and vulnerabilities at the chiplet, interposer, and system-in-package levels. Furthermore, various possible trust validation methods and attack mitigation were proposed for every level of heterogeneous integration. Finally, we shared our vision as a roadmap toward developing security solutions for a secure heterogeneous integration.
Last updated:  2022-08-01
Caulk+: Table-independent lookup arguments
Jim Posen and Assimakis A. Kattis
The recent work of Caulk introduces the security notion of position hiding linkability for vector commitment schemes, providing a zero-knowledge argument that a committed vector's elements comprise a subset of some other committed vector. The protocol has very low cost to the prover in the case where the size $m$ of the subset vector is much smaller than the size $n$ of the one containing it. The asymptotic prover complexity is $O(m^2 + m \log n)$, where the $\log n$ dependence comes from a subprotocol showing that the roots of a blinded polynomial are all $n$th roots of unity. In this work, we show how to simplify this argument, replacing the subprotocol with a polynomial divisibility check and thereby reducing the asymptotic prover complexity to $O(m^2)$, removing any dependence on $n$.
Last updated:  2022-08-01
Key lifting : Multi-key Fully Homomorphic Encryption in plain model without noise flooding in partial decryption
Xiaokang Dai, Wenyuan Wu, and Yong Feng
Multi-key Fully Homomorphic Encryption(\MK) based on Learning With Error(\LWE) usually lifts ciphertexts of different users to new ciphertexts under a common public key to enable homomorphic evaluation. The main obstacle of current \MK schemese in applications is huge ciphertext expansion cost especially in data intensive scenario. For example, for an boolean circuit with input length $N$, multiplication depth $L$, security parameter $\lambda$ , the number of additional encryptions introduced to obtain ciphertext expansion is $O(N\lambda^6L^4)$. In this paper we present a framework to slove this problem that we call Key-Lifting Multi-key Fully Homomorphic Encryption (\KL). By introducing a key lifting procedure, the number of encryptio for a local user is pulled back to $O(N)$. Moreover, current \MK schemes are often based on Common Reference String model(\CRS). In our \textsf{LWE-based} scheme, \CRS is removed by using the leakage resilient property of the leftover hash lemma(\LHL). In particular, we noticed that as long as our encryption scheme is leakage-resilient, the partial decryption does not need to introduce noise flooding technique, and the semantic security of fresh ciphertext can also be guaranteed, which greatly compresses the modulus q and the computational overhead of the entire scheme. Due to the structural properties of polynomial rings, such \textsf{LWE-based} scheme cannot be trivially transplanted to \textsf{RLWE-based} scheme. We give a \textsf{RLWE-based \KL} under Random Oracle Model(\ROM) by introduing a bit commitment protocol.
Last updated:  2022-08-01
Do Not Bound to a Single Position: Near-Optimal Multi-Positional Mismatch Attacks Against Kyber and Saber
Qian Guo and Erik Mårtensson
Misuse resilience is an important security criterion in the evaluation of the NIST Post-quantum cryptography standardization process. In this paper, we propose new key mismatch attacks against Kyber and Saber, NIST's selected scheme for encryption and one of the finalists in the third round of the NIST competition, respectively. Our novel idea is to recover partial information of multiple secret entries in each mismatch oracle call. These multi-positional attacks greatly reduce the expected number of oracle calls needed to fully recover the secret key. They also have significance in side-channel analysis. From the perspective of lower bounds, our new attacks falsify the Huffman bounds proposed in [Qin et al. ASIACRYPT 2021], where a one- positional mismatch adversary is assumed. Our new attacks can be bounded by the Shannon lower bounds, i.e., the entropy of the distribution generating each secret coefficient times the number of secret entries. We call the new attacks "near-optimal" since their query complexities are close to the Shannon lower bounds.
Last updated:  2022-08-01
Secret key generation from Gaussian sources using lattice-based extractors
Laura Luzzi, Cong Ling, and Matthieu R. Bloch
We propose a lattice-based scheme for secret key generation from Gaussian sources in the presence of an eavesdropper, and show that it achieves the strong secret key capacity in the case of degraded source models, as well as the optimal secret key / public communication rate trade-off. The key ingredients of our scheme are a lattice extractor to extract the channel intrinsic randomness, based on the notion of flatness factor, together with a randomized lattice quantization technique to quantize the continuous source. Compared to previous works, we introduce two new notions of flatness factor based on $L^1$ distance and KL divergence, respectively, which are of independent interest. We prove the existence of secrecy-good lattices under $L^1$ distance and KL divergence, whose $L^1$ and KL flatness factors vanish for volume-to-noise ratios up to $2\pi e$. This improves upon the volume-to-noise ratio threshold $2\pi$ of the $L^{\infty}$ flatness factor.
Last updated:  2022-08-01
Ad Hoc (Decentralized) Broadcast, Trace, and Revoke
Ji Luo
Traitor tracing schemes [Chor–Fiat–Naor, Crypto ’94] help content distributors fight against piracy and are defined with the content distributor as a trusted authority having access to the secret keys of all users. While the traditional model caters well to its original motivation, its centralized nature makes it unsuitable for many scenarios. For usage among mutually untrusted parties, a notion of *ad hoc* traitor tracing (naturally with the capability of broadcast and revocation) is proposed and studied in this work. Such a scheme allows users in the system to generate their own public/secret key pairs, without trusting any other entity. To encrypt, a list of public keys is used to identify the set of recipients, and decryption is possible with a secret key for any of the public keys in the list. In addition, there is a tracing algorithm that given a list of recipients’ public keys and a pirate decoder capable of decrypting ciphertexts encrypted to them, identifies at least one recipient whose secret key must have been used to construct the said decoder. Two constructions are presented. The first is based on obfuscation and has constant-size ciphertext, yet its decryption time is linear in the number of recipients. The second is a generic transformation that reduces decryption time at the cost of increased ciphertext size. A lower bound on the trade-off between ciphertext size and decryption time is shown, indicating that the two constructions achieve all possible optimal trade-offs. The lower bound also applies to general attribute-based encryption and may be of independent interest.
Last updated:  2022-08-01
On Security of TrCBC
Debrup Chakraborty and Samir Kundu
TrCBC is a variant of CBC-MAC which appeared in Information Processing Letters, 112(7):302-307, 2012. The authors claimed TrCBC to be a secure message authentication code (MAC) with some interesting properties. If TrCBC is instantiated with a block cipher with block length n, then it requires ⌈λ/n⌉ block cipher calls for authenticating a λ-bit message and requires a single key, which is the block cipher key. The authors state that TrCBC can have tag lengths of size less than n/2. We show that with high probability, an adversary can forge TrCBC with tag length n/2 − 1 with just three queries. The attack that we show can be applied to forge a large class of messages. The authors proved TrCBC to be a pseudorandom function (PRF). A scrutiny of the claimed PRF bound shows that for some recommended values of tag lengths, the bound turns out to be quite large. Thus, the security theorem does not imply security of TrCBC for all recommended tag lengths.
Last updated:  2022-08-01
A note on key control in CSIDH
Antonio Sanso
In this short note we explore a particular behaviour of the CSIDH key exchange that leads to a very special form of (shared) key control via the use of the quadratic twists. This peculiarity contained in CSIDH with regard to quadratic twists was already noted in the original CSDIH work and used in several subsequent papers but we believe spelling out this in the form of an attack might be useful to the wider community.
Last updated:  2022-08-01
The Generalized Montgomery Coordinate: A New Computational Tool for Isogeny-based Cryptography
Tomoki Moriya, Hiroshi Onuki, Yusuke Aikawa, and Tsuyoshi Takagi
Recently, some studies have constructed one-coordinate arithmetics on elliptic curves. For example, formulas of the $x$-coordinate of Montgomery curves, $x$-coordinate of Montgomery$^-$ curves, $w$-coordinate of Edwards curves, $w$-coordinate of Huff's curves, $\omega$-coordinates of twisted Jacobi intersections have been proposed. These formulas are useful for isogeny-based cryptography because of their compactness and efficiency. In this paper, we define a novel function on elliptic curves called the generalized Montgomery coordinate that has the five coordinates described above as special cases. For a generalized Montgomery coordinate, we construct an explicit formula of scalar multiplication that includes the division polynomial, and both a formula of an image point under an isogeny and that of a coefficient of the codomain curve. Finally, we present two applications of the theory of a generalized Montgomery coordinate. The first one is the construction of a new efficient formula to compute isogenies on Montgomery curves. This formula is more efficient than the previous one for high degree isogenies as the $\sqrt{\vphantom{2}}$\'{e}lu's formula in our implementation. The second one is the construction of a new generalized Montgomery coordinate for Montgomery$^-$ curves used for CSURF.
Last updated:  2022-07-31
Random-Index Oblivious RAM
Shai Halevi and Eyal Kushilevitz
We study the notion of Random-index ORAM (RORAM), which is a weak form of ORAM where the Client is limited to asking for (and possibly modifying) random elements of the $N$-items memory, rather than specific ones. That is, whenever the client issues a request, it gets in return a pair $(r,x_r)$ where $r\in_R[N]$ is a random index and $x_r$ is the content of the $r$-th memory item. Then, the client can also modify the content to some new value $x'_r$. We first argue that the limited functionality of RORAM still suffices for certain applications. These include various applications of sampling (or sub-sampling), and in particular the very-large-scale MPC application in the setting of~ Benhamouda et al. (TCC 2020). Clearly, RORAM can be implemented using any ORAM scheme (by the Client selecting the random $r$'s by himself), but the hope is that the limited functionality of RORAM can make it faster and easier to implement than ORAM. Indeed, our main contributions are several RORAM schemes (both of the hierarchical-type and the tree-type) of lighter complexity than that of ORAM.
Last updated:  2022-07-31
FrodoPIR: Simple, Scalable, Single-Server Private Information Retrieval
Alex Davidson, Gonçalo Pestana, and Sofía Celi
We design \textbf{\textsf{FrodoPIR}}~---~a highly configurable, \emph{stateful}, single-server Private Information Retrieval (PIR) scheme that involves an offline phase that is completely \emph{client-independent}. Coupled with small online overheads, it leads to much smaller amortized financial costs on the server-side than previous approaches. In terms of performance for a database of $1$ million $1$KB elements, \textsf{FrodoPIR} requires $< 1$ second for responding to a client query, has a server response size blow-up factor of $< 3.6\times$, and financial costs are $\sim \$1$ for answering $100,000$ client queries. Our experimental analysis is built upon a simple, non-optimized Rust implementation, illustrating that \textsf{FrodoPIR} is eminently suitable for large practical deployments.
Last updated:  2022-07-31
Fast norm computation in smooth-degree Abelian number fields
Daniel J. Bernstein
This paper presents a fast method to compute algebraic norms of integral elements of smooth-degree cyclotomic fields, and, more generally, smooth-degree Galois number fields with commutative Galois groups. The typical scenario arising in $S$-unit searches (for, e.g., class-group computation) is computing a $\Theta(n\log n)$-bit norm of an element of weight $n^{1/2+o(1)}$ in a degree-$n$ field; this method then uses $n(\log n)^{3+o(1)}$ bit operations. An $n(\log n)^{O(1)}$ operation count was already known in two easier special cases: norms from power-of-2 cyclotomic fields via towers of power-of-2 cyclotomic subfields, and norms from multiquadratic fields via towers of multiquadratic subfields. This paper handles more general Abelian fields by identifying tower-compatible integral bases supporting fast multiplication; in particular, there is a synergy between tower-compatible Gauss-period integral bases and a fast-multiplication idea from Rader. As a baseline, this paper also analyzes various standard norm-computation techniques that apply to arbitrary number fields, concluding that all of these techniques use at least $n^2(\log n)^{2+o(1)}$ bit operations in the same scenario, even with fast subroutines for continued fractions and for complex FFTs. Compared to this baseline, algorithms dedicated to smooth-degree Abelian fields find each norm $n/(\log n)^{1+o(1)}$ times faster, and finish norm computations inside $S$-unit searches $n^2/(\log n)^{1+o(1)}$ times faster.
Last updated:  2022-07-31
Secure and Lightweight User Authentication Scheme for Cloud-Aided Internet of Things
Chenyu Wang, Ding Wang, Yihe Duan, and Xiaofeng Tao
The cloud-aided Internet of Things (IoT) overcomes the resource-constrained nature of the traditional IoT and develops rapidly in such fields as smart grid and intelligent transportation. In a cloud-aided IoT system, users can remotely control the IoT devices or send specific instructions to them. When the user's identity is not verified and an adversary delivers malicious instructions to IoT devices, the system's security may be compromised. Besides, the real-time data stored in IoT devices can also be exposed to illegal users, causing security issues. Thus, the authentication mechanism is indispensable. Furthermore, with the exponential growth of interconnected devices, a gateway may connect to mass IoT devices. The efficiency of authentication schemes is easily affected by the computation power of the gateway. Although recent research has proposed many user authentication schemes for IoT, only a dozen schemes are designed for cloud-aided IoT. Therefore, we take a typical scheme (presented at IEEE TDSC 2020) as an example to capture user authentication schemes' common weaknesses and design challenges for cloud-aided IoT. Then, we propose a new secure user authentication scheme for cloud-aided IoT with lightweight computation on gateways. The proposed scheme provides secure access between the remote user and IoT devices with many ideal attributions, such as forward secrecy and multi-factor security. Meanwhile, the security of this scheme is proved under the random oracle model, heuristic analysis, the ProVerif tool and BAN logic. Finally, we compare the proposed scheme with eleven state-of-the-art schemes in security and performance. The results show that the proposed scheme achieves all listed twelve security requirements with minimum computation and storage costs on gateways.
Last updated:  2022-07-31
Fast Unbalanced Private Set Union from Fully Homomorphic Encryption
Binbin Tu, Yu Chen, Qi Liu, and Cong Zhang
Private set union (PSU) allows two parties to compute the union of their sets without revealing anything else. It has found numerous applications in practice. Recently, some computationally efficient PSU protocols have been designed for the balanced case, but a limitation with these protocols is the communication complexity, which scales (super)-linearly with the size of the larger set. This is of particular concern when performing PSU in the unbalanced case, where one party is a constrained device holding a small set, and another is a large service provider holding a large set. In this work, we propose a generic construction of unbalanced PSU from leveled fully homomorphic encryption (FHE) and a newly introduced protocol called permuted matrix Private EQuality Test (pm-PEQT). By instantiating the generic construction, we obtain two secure and fast unbalanced PSU protocols, whose communication complexity is linear in the size of the smaller set, and logarithmic in the larger set. We implement our protocols. Experiments show that our protocols are more efficient than all previous protocols in the unbalanced case. Especially, the larger difference between the size of two sets, the better our protocols perform. For input sets of size $2^{10}$ and $2^{19}$ with 128-bit length items, our PSU takes $2.242$ MB of communication to compute the union. Compared with the state-of-the-art PSU proposed by Jia et al. (Usenix Security 2022), there are $300 \times$ reduction in communication and roughly $30$ - $120 \times$ reduction in computational overhead in WAN/LAN settings.
Last updated:  2022-07-31
Non-Malleable Multi-Party Computation
Fuchun Lin
We study a tamper-tolerant implementation security notion for general purpose Multi-Party Computation (MPC) protocols, as an analogue of the leakage-tolerant notion in the MPC literature. An MPC protocol is tamper-tolerant, or more specifically, non-malleable (with respect to a certain type of tampering) if the processing of the protocol under corruption of parties (and tampering of some ideal resource assumed by the protocol) can be simulated by an ideal world adversary who, after the trusted party spit out the output, further decides how the output for honest parties should be tampered with. Intuitively, we relax the correctness of secure computation in a privacy-preserving way, decoupling the two entangled properties that define secure computation. The rationale behind this relaxation is that even the strongest notion of correctness in MPC allows corrupt parties to substitute wrong inputs to the trusted party and the output is incorrect anyway, maybe the importance of insisting on that the adversary does not further tamper with the incorrect output is overrated, at least for some applications. Various weak privacy notions against malicious adversary play an important role in the study of two-party computation, where full security is hard to achieve efficiently. We begin with the honest majority setting, where efficient constructions for general purpose MPC protocols with full security are well understood assuming secure point-to-point channels. We then focus on non-malleability with respect to tampered secure point-to-point channels. (1) We show achievability of non-malleable MPC against the bounded state tampering adversary in the joint tampering model through a naive compiler approach, exploiting a known construction of interactive non-malleable codes. The construction is currently not efficient and should be understood as showing feasibility in a rather strong tampering model. (2) We show efficient constructions of non-malleable MPC protocols against weaker variants of bounded state tampering adversary in the independent tampering model, where the protocol obtained have the same asymptotic communication complexity as best MPC protocols against honest-but-curious adversary. These are all information-theoretic results and are to be contrasted against impossibility of secure MPC when secure point-to-point channels are compromised. Though general non-malleable MPC in no honest majority setting is beyond the scope of this work, we discuss interesting applications of honest majority non-malleable MPC in the celebrated MPC-in-the-head paradigm. Other than an abstract result concerning non-malleability, we also derive, in standard model where there is no tampering, that strong (ideal/real world) privacy against malicious adversary can be achieved in a conceptually very simple way.
Last updated:  2022-07-30
Allocating Rotational Cryptanalysis based Preimage Attack on 4-round Keccak-224 for Quantum Setting
Runsong Wang, Xuelian Li, Juntao Gao, Hui Li, and Baocang Wang
In this paper, we aim to present a quantum setting oriented preimage attack against 4-round Keccak-224. An important technique we called the allocating rotational cryptanalysis takes the preimage attack into the situation of 2-block preimage recovery. With the conditions on the middle state proposed by Li et al., we use the generic quantum preimage attack to deal with the finding of first preimage block. By using the newly explored propagation of rotational relations, we significantly increase the number of eigenpoints at the end of 4-round modified Keccak-f from 0 to 32, and therefore improving the accuracy of determining the rotational number for a certain rotational counterpart in the quantum setting by more than 10 orders of magnitude. On the basis of the above, we design an efficient unitary oracle operator with only twice calling of the 4-round modified Keccak-f, which costs half of previous results, to mark a rotational counterpart of the second preimage block in order that the second preimage block can be found indirectly from a quickly generated specified search space. As a result on the 4-round Keccak-224: In the classical setting, the preimage attack with the complexity decreased to 2^218 is better than the result based on the pioneered rotational cryptanalysis. In the quantum setting, the amplitude amplification driven preimage attack with a complexity of 2^110 is by far the best dedicated quantum preimage attack. Additionally, the SKW algorithm is applied to the dedicated quantum preimage attack against the 4-round Keccak-224 for the first time, which is exponentially easier to implement in quantum circuit than the former, with a complexity of 2^111.
Last updated:  2022-07-30
WaterBear: Asynchronous BFT with Information-Theoretic Security and Quantum Security
Haibin Zhang, Sisi Duan, Boxin Zhao, and Liehuang Zhu
Show abstract
Designing information-theoretically secure and quantum secure Byzantine fault-tolerant (BFT) protocols in asynchronous environments has been an elusive goal. Critically, all practical asynchronous BFT protocols require using common coins, but we do not have efficient setup-free common coin protocols that are unconditionally secure or quantum secure. We design and implement WaterBear, a family of new asynchronous BFT protocols that are information-theoretically secure or quantum secure. Via extensive evaluation, we show that our protocols are efficient under both failure-free and failure scenarios, achieving comparable performance to the state-of-the-art asynchronous BFT protocols with much weaker security guarantees. To achieve the goal, we have designed much more efficient asynchronous binary agreement (ABA) protocols from local coins and their reproposable ABA counterparts. We have also built more efficient ABA protocols from weak common coins and perfect common coins. These ABA protocols can be readily used to improve various high-level Byzantine-resilient primitives, such as asynchronous distributed key generation and BFT assuming trusted setup.
Last updated:  2022-07-30
Private Set Operations from Multi-Query Reverse Private Membership Test
Yu Chen, Min Zhang, Cong Zhang, and Minglang Dong
Private set operations allow two parties to perform secure computation on two private sets, such as intersection or union related functions. In this paper, we identify a framework for performing private set operations. At the technical core of our framework is multi-query reverse private membership test (mqRPMT), which is a natural extension of RPMT recently proposed by Kolesnikov et al.~\cite{KRTW-ASIACRYPT-2019}. In mqRPMT, a client with a vector $X = (x_1, \dots, x_n)$ interacts with a server holding a set $Y$. As a result, the server only learns a bit vector $(e_1, \dots, e_n)$ indicating whether $x_i \in Y$ but without knowing the value of $x_i$, while the client learns nothing. We present two constructions of mqRPMT from newly introduced cryptographic primitive and protocol. One is based on commutative weak pseudorandom function (cwPRF), the other is based on permuted oblivious pseudorandom functions (pOPRF). Both cwPRF and pOPRF can be instantiated from the decisional Diffie-Hellman like assumptions in the random oracle model. We also introduce a slight weak version of mqRPMT dubbed mqRPMT$^*$, in which the client learns the cardinality of $X \cap Y$. We show mqRPMT$^*$ can be build from a category of multi-query private membership test (mqPMT) called Sigma-mqPMT, which in turn can be realized from DDH-like assumptions or oblivious polynomial evaluation. This makes the first step towards establishing the relation between mqPMT and mqRPMT. We demonstrate the practicality of our framework with implementations. By plugging our cwPRF-based mqRPMT to the general framework, we obtain various efficient PSO protocols that are competitive or superior to the-state-of-art protocols. For cardinality functionality, our protocol achieves a $1.17-6.62\times$ speedup in running time and a $10.85-14.80\times$ shrinking in communication cost. For cardinality-with-sum functionality, our protocol achieves a $8-40\times$ speedup in running time and a $10 \times$ shrinking in communication cost. For union functionality, our protocol achieves strict linear complexity. Among all the existing PSU protocols, it requires the least concrete communication cost, and is also the fastest one in the WAN setting. Specifically, for input set of size $2^{20}$, our PSU protocol requires roughly 100 MB bandwidth, and 58 seconds using 4 threads in the LAN setting. For private-ID functionality, our protocol achieves a $1.39-4.75\times$ speedup in running time. Moreover, by plugging our FHE-based mqRPMT$^*$ to the general framework, we obtain a PSU$^*$ protocol (the sender additionally learns the intersection size) suitable for unbalanced setting, whose communication complexity is linear in the size of the smaller set, and logarithmic in the larger set.
Last updated:  2022-07-30
Efficient Proof of RAM Programs from Any Public-Coin Zero-Knowledge System
Cyprien Delpech de Saint Guilhem, Emmanuela Orsini, Titouan Tanguy, and Michiel Verbauwhede
We show a compiler that allows to prove the correct execution of RAM programs using any zero-knowledge system for circuit satisfiability. At the core of this work is an arithmetic circuit which verifies the consistency of a list of memory access tuples in zero-knowledge. Using such a circuit, we obtain the first constant-round and concretely efficient zero-knowledge proof protocol for RAM programs using any stateless zero-knowledge proof system for Boolean or arithmetic circuits. Both the communication complexity and the prover and verifier run times asymptotically scale linearly in the size of the memory and the run time of the RAM program; we demonstrate concrete efficiency with performance results of our C++ implementation. We concretely instantiate our construction with an efficient MPC-in-the-Head proof system, Limbo (ACM CCS 2021). The C++ implementation of our access protocol extends that of Limbo and provides interactive proofs with 40 bits of statistical security with an amortized cost of 0.42ms of prover time and 2.8KB of communication per memory access, independently of the size of the memory; with multi-threading, this cost is reduced to 0.12ms and 1.8KB respectively. This performance of our public-coin protocol approaches that of private-coin protocol BubbleRAM (ACM CCS 2020, 0.15ms and 1.5KB per access).
Last updated:  2022-07-30
Paras - A Private NFT Protocol
Vanishree Rao
Non-fungible tokens (NFTs) are a blockchain application that has recently witnessed significant success. However, NFT marketplaces are majorly built on popular blockchain platforms that do not provide privacy tools. As a result, NFTs are easily visible to everyone. This has naturally given rise to various issues, including stolen/duplicate NFTs and attacks like shill trading. Furthermore, this architecture fails to reflect the real-life privacy notion as it digitizes unique physical goods. In this project, we build Paras - a blockchain-agnostic protocol that offers privacy to NFTs. Specifically, one may hide the real NFTs and only display a reference to them on marketplaces, hide seller and bidder identities, hide bid values and user wallet balances. Paras is based on cryptographic primitives, such as, threshold encryption and robust secret sharing. It does not rely on any trusted execution environments for security, unlike some existing protocols in this direction.
Last updated:  2022-07-30
Pushing the Limits of Generic Side-Channel Attacks on LWE-based KEMs - Parallel PC Oracle Attacks on Kyber KEM and Beyond
Gokulnath Rajendran, Prasanna Ravi, Jan-Pieter D'Anvers, Shivam Bhasin, and Anupam Chattopadhyay
In this work, we propose generic and novel adaptations to the binary Plaintext-Checking (PC) oracle based side-channel attacks for Kyber KEM. Binary PC oracle-based side-channel attacks are fairly generic and easy to mount on a given target, as the attacker requires very minimal information about the target device. However, these attacks have an inherent disadvantage of requiring a few thousand traces to perform full key recovery, as they only recover a single bit of information per trace. We propose novel parallel PC oracle based side-channel attacks, which are capable of recovering an arbitrary P number of bits of information about the secret key in a single trace. We experimentally validated our attacks on the fastest implementation of unprotected Kyber KEM in the pqm4 library on the ARM Cortex-M4 microcontroller. Our experiments yielded improvements in the range of 2.89x and 7.65x in the number of queries, compared to state-of-the-art binary PC oracle attacks, while arbitrarily higher improvements are possible for a motivated attacker, given the generic nature of our attack. Finally, we also conduct a thorough study of the capability of our attack in different attack scenarios, based on the presence/absence of a clone device, and also partial key recovery. We also show that our proposed attacks are able to achieve the lowest number of queries for key recovery, even over implementations protected with low-cost countermeasures such as shuffling. Our work therefore, concretely demonstrates the power of PC oracle attacks on Kyber KEM, thereby stressing the need for concrete countermeasures such as masking.
Last updated:  2022-07-29
$\mathsf{PEReDi}$: Privacy-Enhanced, Regulated and Distributed Central Bank Digital Currencies
Aggelos Kiayias, Markulf Kohlweiss, and Amirreza Sarencheh
Central Bank Digital Currencies (CBDCs) aspire to offer a digital replacement for physical cash and as such need to tackle two fundamental requirements that are in conflict. On the one hand, it is desired they are $\textit{private}$ so that a financial ``panopticon'' is avoided, while on the other, they should be $\textit{regulation friendly}$ in the sense of facilitating any threshold-limiting, tracing, and counterparty auditing functionality that is necessary to comply with regulations such as Know Your Customer (KYC), Anti Money Laundering (AML) and Combating Financing of Terrorism (CFT) as well as financial stability considerations. In this work, we put forth a new model for CBDCs and an efficient construction that, for the first time, fully addresses these issues simultaneously. Moreover, recognizing the importance of avoiding a $\textit{single point of failure}$, our construction is distributed so that all its properties can withstand a suitably bounded minority of participating entities getting corrupted by an adversary. Achieving all the above properties efficiently is technically involved; among others, our construction uses suitable cryptographic tools to thwart man-in-the-middle attacks, it showcases a novel traceability mechanism with significant performance gains compared to previously known techniques and, perhaps surprisingly, shows how to obviate Byzantine agreement or broadcast from the optimistic execution path of a payment, something that results in an essentially optimal communication pattern and communication overhead when the sender and receiver are honest. Going beyond ``simple'' payments, we also discuss how our scheme can facilitate one-off large transfers complying with Know Your Transaction (KYT) disclosure requirements. Our CBDC concept is expressed and realized in the Universal Composition (UC) framework providing in this way a modular and secure way to embed it within a larger financial ecosystem.
Last updated:  2022-07-29
Multiple Noisy Private Remote Source Observations for Secure Function Computation
Onur Gunlu, Matthieu Bloch, and Rafael F. Schaefer
The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function computation problem include 1) privacy leakage to an eavesdropper is measured with respect to the remote source rather than the transmitting terminals' observed sequences; 2) the information leakage to a fusion center with respect to the remote source is considered as another privacy leakage metric; 3) two transmitting node observations are used to compute a function. Inner and outer bounds on the rate regions are derived for lossless single-function computation with two transmitting nodes, which recover previous results in the literature, and for special cases that consider invertible functions simplified bounds are established.
Last updated:  2022-07-29
Bootstrapping in FHEW-like Cryptosystems
Daniele Micciancio and Yuriy Polyakov
FHEW and TFHE are fully homomorphic encryption (FHE) cryptosystems that can evaluate arbitrary Boolean circuits on encrypted data by bootstrapping after each gate evaluation. The FHEW cryptosystem was originally designed based on standard (Ring, circular secure) LWE assumptions, and its initial implementation was able to run bootstrapping in less than 1 second. The TFHE cryptosystem used somewhat stronger assumptions, such as (Ring, circular secure) LWE over the torus with binary secret distribution, and applied several other optimizations to reduce the bootstrapping runtime to less than 0.1 second. Up to now, the gap between the underlying security assumptions prevented a fair comparison of the cryptosystems for the same security settings. We present a unified framework that includes the original and extended variants of both FHEW and TFHE cryptosystems, and implement it in the open-source PALISADE lattice cryptography library using modular arithmetic. Our analysis shows that the main distinction between the cryptosystems is the bootstrapping procedure used: Alperin-Sherif--Peikert (AP) for FHEW vs. Gama--Izabachene--Nguyen--Xie (GINX) for TFHE. All other algorithmic optimizations in TFHE equally apply to both cryptosystems. The GINX bootstrapping method makes essential the use of binary secrets, and cannot be directly applied to other secret distributions. In the process of comparing the two schemes, we present a simple, lightweight method to extend GINX bootstrapping (e.g., as employed by TFHE) to ternary uniform and Gaussian secret distributions, which are included in the HE community security standard. Our comparison of the AP and GINX bootstrapping methods for different secret distributions suggests that the TFHE/GINX cryptosystem provides better performance for binary and ternary secrets while FHEW/AP is faster for Gaussian secrets. We make a recommendation to consider the variants of FHEW and TFHE cryptosystems based on ternary and Gaussian secrets for standardization by the HE community.
Last updated:  2022-07-29
MR-DSS – Smaller MinRank-based (Ring-)Signatures
Emanuele Bellini, Andre Esser, Carlo Sanna, and Javier Verbel
In the light of NIST’s announced reopening of the call for digital signature proposals in 2023 due to lacking diversity, there is a strong need for constructions based on other established hardness assumptions. In this work we construct a new post-quantum secure digital signature scheme based on the $MinRank$ problem, a problem with a long history of applications in cryptanalysis that led to a strong belief in its hardness. Initially following a design by Courtois (Asiacrypt '01) based on the Fiat--Shamir transform, we make use of several recent developments in the design of sigma protocols to reduce signature size and improve efficiency. This includes the recently introduced $sigma \; protocol \; with \; helper$ paradigm (Eurocrypt '19) and combinations with $cut$-$and$-$choose$ techniques (CCS '18). Moreover, we introduce several improvements to the core of the scheme to further reduce its signature size.
Last updated:  2022-07-29
Quantum Analysis of AES
Kyungbae Jang, Anubhab Baksi, Gyeongju Song, Hyunji Kim, Hwajeong Seo, and Anupam Chattopadhyay
Quantum computing is considered among the next big leaps in the computer science. While a fully functional quantum computer is still in the future, there is an ever-growing need to evaluate the security of the secret-key ciphers against a potent quantum adversary. Keeping this in mind, our work explores the key recovery attack using the Grover's search on the three variants of AES (-128, -192, -256) with respect to the quantum implementation and the quantum key search using the Grover's algorithm. We develop a pool of implementations, by mostly reducing the circuit depth metrics. We consider various strategies for optimization, as well as make use of the state-of-the-art advancements in the relevant fields. In a nutshell, we present the least Toffoli depth and full depth implementations of AES, thereby improving from Zou et al.'s Asiacrypt'20 paper by more than 98 percent for all variants of AES. Our qubit count - Toffoli depth product is improved from theirs by more than 75 percent. Furthermore, we analyze the Jaques et al.'s Eurocrypt'20 implementations in details, fix its bugs and report corrected benchmarks. To the best of our finding, our work improves from all the previous works (including the recent Eprint'22 paper by Huang and Sun).
Last updated:  2022-07-29
Arithmetization of Σ¹₁ relations in Halo 2
Morgan Thomas
Orbis Labs presents a method for compiling (“arithmetizing”) relations, expressed as Σ11 formulas in the language of rings, into Halo 2 arithmetic circuits. This method offers the possibility of creating arithmetic circuits without laborious and error-prone manual circuit design and implementation, by instead expressing the relation to be arithmetized in a concise mathematical notation and generating the circuit based on that expression.
Last updated:  2022-07-29
Keyed Streebog is a secure PRF and MAC
Vitaly Kiryukhin
One of the most popular ways to turn a keyless hash function into a keyed one is the HMAC algorithm. This approach is too expensive in some cases due to double hashing. Excessive overhead can sometimes be avoided by using certain features of the hash function itself. The paper presents a simple and safe way to create a keyed cryptoalgorithm (conventionally called "Streebog-K") from hash function Streebog $\mathsf{H}(M)$. Let $K$ be a secret key, then $\mathsf{KH}(K,M)=\mathsf{H}(K||M)$ is a secure pseudorandom function (PRF) and, therefore, a good message authentification code (MAC). The proof is obtained by reduction of the security of the presented construction to the resistance of the underlying compression function to the related key attacks (PRF-RKA). The security bounds of Streebog-K are essentially the same as those of HMAC-Streebog, but the computing speed doubles when short messages are used.
Last updated:  2022-07-28
Long Live The Honey Badger: Robust Asynchronous DPSS and its Applications
Thomas Yurek, Zhuolun Xiang, Yu Xia, and Andrew Miller
Secret sharing is an essential tool for many distributed applications, including distributed key generation and multiparty computation. For many practical applications, we would like to tolerate network churn, meaning participants can dynamically enter and leave the pool of protocol participants as they please. Such protocols, called Dynamic-committee Proactive Secret Sharing (DPSS) have recently been studied; however, existing DPSS protocols do not gracefully handle faults: the presence of even one unexpectedly slow node can often slow down the whole protocol by a factor of $O(n)$. In this work, we explore optimally fault-tolerant asynchronous DPSS that is not slowed down by crash faults and even handles byzantine faults while maintaining the same performance. We first introduce the first high-threshold DPSS, which offers favorable characteristics relative to prior non-synchronous works in the presence of faults while simultaneously supporting higher privacy thresholds. We then batch-amortize this scheme along with a parallel non-high-threshold scheme which achieves optimal bandwidth characteristics. We implement our schemes and demonstrate that they can compete with prior work in best-case performance while outperforming it in non-optimal settings.
Last updated:  2022-07-28
The Need for Speed: A Fast Guessing Entropy Calculation for Deep Learning-based SCA
Guilherme Perin, Lichao Wu, and Stjepan Picek
The adoption of deep neural networks for profiling side-channel attacks (SCA) opened new perspectives for leakage detection. Recent publications showed that cryptographic implementations featuring different countermeasures could be broken without feature selection or trace preprocessing. This success comes with a high price: extensive hyperparameter search to find optimal deep learning models. As deep learning models usually suffer from overfitting due to their high fitting capacity, it is crucial to avoid over-training regimes, which require a correct number of epochs. For that, \textit{early stopping} is employed as an efficient regularization method that requires a consistent validation metric. Although guessing entropy is a highly informative metric for profiling SCA, it is time-consuming, especially if computed for all epochs during training and the number of validation traces is significantly large. This paper shows that guessing entropy can be efficiently computed during training by reducing the number of validation traces without affecting the efficiency of early stopping decisions. Our solution significantly speeds up the process, impacting hyperparameter search and overall profiling attack performances. Our fast guessing entropy calculation is up to 16$\times$ faster, resulting in more hyperparameter tuning experiments and allowing security evaluators to find more efficient deep learning model.
Last updated:  2022-07-28
Related-key attacks on the compression function of Streebog
Vitaly Kiryukhin
Related-key attacks against block ciphers are often considered unrealistic. In practice, as far as possible, the existence of a known "relation" between the secret encryption keys is avoided. Despite this, related keys arise directly in some widely used keyed hash functions. This is especially true for HMAC-Streebog, where known constants and manipulated parameters are added to the secret key. The relation is determined by addition modulo $2$ and $2^{n}$. The security of HMAC reduces to the properties of the underlying compression function. Therefore, as an initial analysis we propose key-recovery methods for 10 and 11 rounds (out of 12) of Streebog compression function in the related-key setting. The result shows that Streebog successfully resists attacks even in the model with such powerful adversaries.
Last updated:  2022-07-28
Certified Everlasting Functional Encryption
Taiga Hiroka, Tomoyuki Morimae, Ryo Nishimaki, and Takashi Yamakawa
Computational security in cryptography has a risk that computational assumptions underlying the security are broken in the future. One solution is to construct information-theoretically-secure protocols, but many cryptographic primitives are known to be impossible (or unlikely) to have information-theoretical security even in the quantum world. A nice compromise (intrinsic to quantum) is certified everlasting security, which roughly means the following. A receiver with possession of quantum encrypted data can issue a certificate that shows that the receiver has deleted the encrypted data. If the certificate is valid, the security is guaranteed even if the receiver becomes computationally unbounded. Although several cryptographic primitives, such as commitments and zero-knowledge, have been made certified everlasting secure, there are many other important primitives that are not known to be certified everlasting secure. In this paper, we introduce certified everlasting FE. In this primitive, the receiver with the ciphertext of a message $m$ and the functional decryption key of a function $f$ can obtain $f(m)$ and nothing else. The security holds even if the adversary becomes computationally unbounded after issuing a valid certificate. We, first, construct certified everlasting FE for P/poly circuits where only a single key query is allowed for the adversary. We, then, extend it to $q$-bounded one for NC1 circuits where $q$-bounded means that $q$ key queries are allowed for the adversary with an a priori bounded polynomial $q$. For the construction of certified everlasting FE, we introduce and construct certified everlasting versions of secret-key encryption, public-key encryption, receiver non-committing encryption, and a garbling scheme, which are of independent interest.
Last updated:  2022-07-27
Zero-Knowledge Proofs on Secret-Shared Data via Fully Linear PCPs
Dan Boneh, Elette Boyle, Henry Corrigan-Gibbs, Niv Gilboa, and Yuval Ishai
We introduce and study the notion of fully linear probabilistically checkable proof systems. In such a proof system, the verifier can make a small number of linear queries that apply jointly to the input and a proof vector. Our new type of proof system is motivated by applications in which the input statement is not fully available to any single verifier, but can still be efficiently accessed via linear queries. This situation arises in scenarios where the input is partitioned or secret-shared between two or more parties, or alternatively is encoded using an additively homomorphic encryption or commitment scheme. This setting appears in the context of secure messaging platforms, verifiable outsourced computation, PIR writing, private computation of aggregate statistics, and secure multiparty computation (MPC). In all these applications, there is a need for fully linear proof systems with short proofs. While several efficient constructions of fully linear proof systems are implicit in the interactive proofs literature, many questions about their complexity are open. We present several new constructions of fully linear zero-knowledge proof systems with sublinear proof size for "simple" or "structured" languages. For example, in the non-interactive setting of fully linear PCPs, we show how to prove that an input vector $x\in\mathbb{F}^n$ satisfies a single degree-2 equation with a proof of size $O(\sqrt n)$ and $O(\sqrt n)$ linear queries, which we show to be optimal. More generally, for languages that can be recognized by systems of constant-degree equations, we can reduce the proof size to $O(\log n)$ at the cost of $O(\log n)$ rounds of interaction. We use our new proof systems to construct new short zero-knowledge proofs on distributed and secret-shared data. These proofs can be used to improve the performance of many of the example systems mentioned above. Finally, we observe that zero-knowledge proofs on distributed data provide a general-purpose tool for protecting protocols for secure multiparty computation (MPC) against malicious parties. Applying our short fully linear PCPs to "natural" MPC protocols in the honest-majority setting, we can achieve unconditional protection against malicious parties with sublinear additive communication cost. We use this to improve the communication complexity of recent honest-majority MPC protocols. For instance, using any pseudorandom generator, we obtain a 3-party protocol for Boolean circuits in which the amortized communication cost is only one bit per AND gate per party (compared to 7 bits in the best previous protocol), matching the best known protocols for semi-honest adversaries.
Last updated:  2022-07-27
A Note on Key Ranking for Optimal Collision Side-Channel Attacks
Cezary Glowacz
In "Optimal collision side-channel attacks" ( we studied collision side-channel attacks and derived an optimal distinguisher for key ranking. In this note we show that the problem of key ranking using this distinguisher is NP-hard and we provide estimates of lower bounds for secret key ranks in collision side-channel attacks.
Last updated:  2022-07-27
Code Equivalence in the Sum-Rank Metric: Hardness and Completeness
Giuseppe D'Alconzo
In this work, we define and study equivalence problems for sum-rank codes, giving their formulation in terms of tensors. Moreover, we introduce the concept of generating tensors of a sum-rank code, a direct generalization of the generating matrix for a linear code endowed with the Hamming metric. In this way, we embrace well-known definitions and problems for Hamming and rank metric codes. Finally, we prove the TI-completeness of code equivalence for rank and sum-rank codes, and hence, in the future, these problems could be used in the design of post-quantum schemes.
Last updated:  2022-07-27
Plactic key agreement
Daniel R. L. Brown
Plactic key agreement is a new key agreement scheme that uses Knuth’s multiplication of semistandard tableaus from combinatorial algebra. The security of plactic key agreement relies on the difficulty of some computational problems, such as division of semistandard tableaus. Division by erosion uses backtracking to divide tableaus. Division by erosion is estimated to be infeasible against public keys of 768 or more bytes. If division by erosion is the best attack against plactic key agreement, then secure plactic key agreement could be practical.
Last updated:  2022-07-27
On the Computational Hardness of the Code Equivalence Problem in Cryptography
Alessandro Barenghi, Jean-Francois Biasse, Edoardo Persichetti, and Paolo Santini
Code equivalence is a well-known concept in coding theory. Recently, literature saw an increased interest in this notion, due to the introduction of protocols based on the hardness of finding the equivalence between two linear codes. In this paper, we analyze the security of code equivalence, with a special focus on the hardest instances, in the interest of cryptographic usage. Our work stems from a thorough review of existing literature, identifies the various types of solvers for the problem, and provides a precise complexity analysis, where previously absent. Furthermore, we are able to improve on the state of the art, providing more efficient algorithm variations, for which we include numerical simulation data. Our results include also a dedicated method for solving code equivalence with a quantum algorithm, as well as a refinement of quantum Information-Set Decoding (ISD) algorithms. In the end, the goal of this paper is to provide a complete, single point of access, which can be used as a tool for designing schemes that rely on the code equivalence problem.
Last updated:  2022-07-27
On Linear Complexity of Finite Sequences : Coding Theory and Applications to Cryptography
Edoardo Persichetti and Tovohery Randrianarisoa
We define two metrics on vector spaces over a finite field using the linear complexity of finite sequences. We then develop coding theory notions for these metrics and study their properties. We give a Singleton-like bound as well as constructions of subspaces achieving this bound. We also provide an asymptotic Gilbert-Varshamov-like bound for random subspaces. We show how to reduce the problem of finding codewords with given Hamming weight into a problem of finding a vector of a given linear complexity. This implies that our new metric can be used for cryptography in a similar way to what is currently done in the code-based setting.
Last updated:  2022-07-27
PROLEAD - A Probing-Based Hardware Leakage Detection Tool
Nicolai Müller and Amir Moradi
Even today, SCA attacks pose a serious threat to the security of cryptographic implementations fabricated with low-power and nano-scale feature technologies. Fortunately, the masking countermeasures offer reliable protection against such attacks based on simple security assumptions. However, the practical application of masking to a cryptographic algorithm is not trivial, and the designer may overlook possible security flaws, especially when masking a complex circuit. Moreover, abstract models like probing security allow formal verification tools to evaluate masked implementations. However, this is computationally too expensive when dealing with circuits that are not based on composable gadgets. Unfortunately, using composable gadgets comes at some area overhead. As a result, such tools can only evaluate subcircuits, not their compositions, which can become the Achilles' heel of such masked implementations. In this work, we apply logic simulations to evaluate the security of masked implementations which are not necessarily based on composable gadgets. We developed PROLEAD, an automated tool analyzing the statistical independence of simulated intermediates probed by a robust probing adversary. Compared to the state of the art, our approach (1) does not require any power model as only the state of a gate-level netlist is simulated, (2) can handle masked full cipher implementations, and (3) can detect flaws related to the combined occurrence of glitches and transitions as well as higher-order multivariate leakages. With PROLEAD, we can evaluate masked implementations that are too complex for existing formal verification tools while being in line with the robust probing model. Through PROLEAD, we have detected security flaws in several publicly-available masked implementations, which have been claimed to be robust probing secure.
Last updated:  2022-07-27
WeRLman: To Tackle Whale (Transactions), Go Deep (RL)
Roi Bar-Zur, Ameer Abu-Hanna, Ittay Eyal, and Aviv Tamar
The security of proof-of-work blockchain protocols critically relies on incentives. Their operators, called miners, receive rewards for creating blocks containing user-generated transactions. Each block rewards its creator with newly minted tokens and with transaction fees paid by the users. The protocol stability is violated if any of the miners surpasses a threshold ratio of the computational power; she is then motivated to deviate with selfish mining and increase her rewards. Previous analyses of selfish mining strategies assumed constant rewards. But with statistics from operational systems, we show that there are occasional whales- blocks with exceptional rewards. Modeling this behavior implies a state-space that grows exponentially with the parameters, becoming prohibitively large for existing analysis tools. We present the WeRLman framework to analyze such models. WeRLman uses deep Reinforcement Learning (RL), inspired by the state-of-the-art AlphaGo Zero algorithm. Directly extending AlphaGo Zero to a stochastic model leads to high sampling noise, which is detrimental to the learning process. Therefore, WeRLman employs novel variance reduction techniques by exploiting the recurrent nature of the system and prior knowledge of transition probabilities. Evaluating WeRLman against models we can accurately solve demonstrates it achieves unprecedented accuracy in deep RL for blockchain. We use WeRLman to analyze the incentives of a rational miner in various settings and upper-bound the security threshold of Bitcoin-like blockchains. We show, for the first time, a negative relationship between fee variability and the security threshold. The previously known bound, with constant rewards, stands at 0.25. We show that considering whale transactions reduces this threshold considerably. In particular, with Bitcoin historical fees and its future minting policy, its threshold for deviation will drop to 0.2 in 10 years, 0.17 in 20 years, and to 0.12 in 30 years. With recent fees from the Ethereum smart-contract platform, the threshold drops to 0.17. These are below the common sizes of large miners.
Last updated:  2022-07-27
PayMo: Payment Channels For Monero
Sri AravindaKrishnan Thyagarajan, Giulio Malavolta, Fritz Schmidt, and Dominique Schröder
Decentralized cryptocurrencies still suffer from three interrelated weaknesses: Low transaction rates, high transaction fees, and long confirmation times. Payment Channels promise to be a solution to these issues, and many constructions for real-life cryptocurrencies, such as Bitcoin, are known. Somewhat surprisingly, no such solution is known for Monero, the largest privacy-preserving cryptocurrency, without requiring system-wide changes like a hard-fork of its blockchain. In this work, we close this gap by presenting \textsc{PayMo}, the first payment channel protocol that is fully compatible with Monero. \textsc{PayMo} does not require any modification of Monero and can be readily used to perform off-chain payments. Notably, transactions in \textsc{PayMo} are identical to standard transactions in Monero, therefore not hampering the coins' fungibility. Using \textsc{PayMo}, we also construct the first fully compatible secure atomic-swap protocol for Monero: One can now securely swap a token of Monero with a token of several major cryptocurrencies such as Bitcoin, Ethereum, Ripple, Cardano, etc. Before our work, it was not known how to implement secure atomic swaps protocols for Monero without forcing a hard fork. Our main technical contribution is a new construction of an efficient verifiable timed linkable ring signature, where signatures can be hidden for a pre-determined amount of time, in a verifiable way. Our scheme is fully compatible with the transaction scheme of Monero and it might be of independent interest. We implemented \textsc{PayMo} and our results show that, even with high network latency and with a single CPU core, two regular users can perform up to 93500 payments over a span of 2 minutes (the block production rate of Monero). This is approximately five orders of magnitude improvement over the current payment rate of Monero.
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