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23 February 2024
Shiyao Chen, Jian Guo, Eik List, Danping Shi, Tianyu Zhang
Since the seminal works by Sasaki and Aoki, Meet-in-the-Middle (MITM) attacks are recognized as an effective technique for preimage and collision attacks on hash functions. At Eurocrypt 2021, Bao et al. automated MITM attacks on AES-like hashing and improved upon the best manual result. The attack framework has been furnished by subsequent works, yet far from complete. This paper elucidates three key contributions dedicated in further generalizing the idea of MITM and refining the automatic model on AES-like hashing. (1) We introduce S-box linearization to MITM pseudo-preimage attacks on AES-like hashing. The technique suits perfectly with superposition states to preserve information after S-box with an affordable cost. (2) We propose distributed initial structures, an extension on the original concept of initial states, that selects initial degrees of freedom in a more versatile manner to enlarge the search space. (3) We exploit the structural similarities between encryption and key schedule in constructions (e.g. Whirlpool and Streebog) to model propagations more accurately and avoid repeated costs. Weaponed with these innovative techniques, we further empower the MITM framework and improve the attack results on AES-like designs for preimage and collision. We obtain the first preimage attacks on 10-round AES-192, 10-round Rijndael-192/256, and 7.75-round Whirlpool, reduced time and/or memory complexities for preimage attacks on 5-, 6-round Whirlpool and 7.5-, 8.5-round Streebog, as well as improved collision attacks on 6- and 6.5-round Whirlpool.
Robin Leander Schröder, Stefan Gast, Qian Guo
We uncover a critical side-channel vulnerability in the Hamming Quasi-Cyclic (HQC) round 4 optimized implementation arising due to the use of the modulo operator. In some cases, compilers optimize uses of the modulo operator with compile-time known divisors into constant-time Barrett reductions. However, this optimization is not guaranteed: for example, when a modulo operation is used in a loop the compiler may emit division (div) instructions which have variable execution time depending on the numerator. When the numerator depends on secret data, this may yield a timing side-channel. We name vulnerabilities of this kind Divide and
Surrender (DaS) vulnerabilities.
For processors supporting Simultaneous Multithreading (SMT) we propose a new approach called DIV-SMT which enables precisely measuring small division timing variations using scheduler and/or execution unit contention. We show that using only 100 such side-channel traces we can build a Plaintext-Checking (PC) oracle with above 90% accuracy. Our approach may also prove applicable to other instances of the DaS vulnerability, such as KyberSlash. We stress that exploitation with DIV-SMT requires co-location of the attacker on the same physical core as the victim.
We then apply our methodology to HQC and present a novel way to recover HQC secret keys faster, achieving an 8-fold decrease in the number of idealized oracle queries when compared to previous approaches. Our new PC oracle attack uses our newly developed Zero Tester method to quickly determine whether an entire block of bits contains only zero-bits. The Zero Tester method enables the DIV-SMT powered attack on HQC-128 to complete in under 2 minutes on our targeted AMD Zen2
machine.
Mathieu Degré, Patrick Derbez, Lucie Lahaye, André Schrottenloher
This paper focuses on the cryptanalysis of the ASCON family using automatic tools. We analyze two different problems with the goal to obtain new modelings, both simpler and less computationally heavy than previous works (all our models require only a small amount of code and run on regular desktop computers).
The first problem is the search for Meet-in-the-middle attacks on reduced-round ASCON-Hash. Starting from the MILP modeling of Qin et al. (EUROCRYPT 2023 & ePrint 2023), we rephrase the problem in SAT, which accelerates significantly the solving time and removes the need for the ``weak diffusion structure'' heuristic. This allows us to reduce the memory complexity of Qin et al.'s attacks and to prove some optimality results.
The second problem is the search for lower bounds on the probability of differential characteristics for the ASCON permutation. We introduce a lossy MILP encoding of the propagation rules based on the Hamming weight, in order to find quickly lower bounds which are comparable to the state of the art. We find a small improvement over the existing bound on 7 rounds.
The first problem is the search for Meet-in-the-middle attacks on reduced-round ASCON-Hash. Starting from the MILP modeling of Qin et al. (EUROCRYPT 2023 & ePrint 2023), we rephrase the problem in SAT, which accelerates significantly the solving time and removes the need for the ``weak diffusion structure'' heuristic. This allows us to reduce the memory complexity of Qin et al.'s attacks and to prove some optimality results.
The second problem is the search for lower bounds on the probability of differential characteristics for the ASCON permutation. We introduce a lossy MILP encoding of the propagation rules based on the Hamming weight, in order to find quickly lower bounds which are comparable to the state of the art. We find a small improvement over the existing bound on 7 rounds.
ABHISAR, Madhav Yadav, Girish Mishra
This research extends Abadi and Andersen's exploration of neural networks using secret keys for information protection in multiagent systems. Focusing on enhancing confidentiality properties, we employ end-to-end adversarial training with neural networks Alice, Bob, and Eve. Unlike prior work limited to 64-bit messages, our study spans message sizes from 4 to 1024 bits, varying batch sizes and training steps. An innovative aspect involves training model Bob to approach a minimal error value close to zero and examining its effect on the feasibility of the model. This research unveils the neural networks' adaptability and scalability in encryption and decryption across diverse scenarios, offering valuable insights into their optimization potential for secure communication.
Yiming Gao, Jinghui Wang, Honggang Hu, Binang He
The Hidden Number Problem (HNP) has found extensive applications in side-channel attacks against cryptographic schemes, such as ECDSA and Diffie-Hellman. There are two primary algorithmic approaches to solving the HNP: lattice-based attacks and Fourier analysis-based attacks. Lattice-based attacks exhibit better efficiency and require fewer samples when sufficiently long substrings of the nonces are known. However, they face significant challenges when only a small fraction of the nonce is leaked, such as 1-bit leakage, and their performance degrades in the presence of errors.
In this paper, we address an open question by introducing an algorithmic tradeoff that significantly bridges the gap between these two approaches. By introducing a parameter $x$ to modify Albrecht and Heninger's lattice, the lattice dimension is reduced by approximately $(\log_2{x})/ l$, where $l$ represents the number of leaked bits. We present a series of new methods, including the interval reduction algorithm, several predicates, and the pre-screening technique. Furthermore, we extend our algorithms to solve the HNP with erroneous input. Our attack outperforms existing state-of-the-art lattice-based attacks against ECDSA. We break several records including 1-bit and less than 1-bit leakage on a 160-bit curve, while the best previous lattice-based attack for 1-bit leakage was conducted only on a 112-bit curve.
In this paper, we address an open question by introducing an algorithmic tradeoff that significantly bridges the gap between these two approaches. By introducing a parameter $x$ to modify Albrecht and Heninger's lattice, the lattice dimension is reduced by approximately $(\log_2{x})/ l$, where $l$ represents the number of leaked bits. We present a series of new methods, including the interval reduction algorithm, several predicates, and the pre-screening technique. Furthermore, we extend our algorithms to solve the HNP with erroneous input. Our attack outperforms existing state-of-the-art lattice-based attacks against ECDSA. We break several records including 1-bit and less than 1-bit leakage on a 160-bit curve, while the best previous lattice-based attack for 1-bit leakage was conducted only on a 112-bit curve.
Kostas Kryptos Chalkias, Jonas Lindstrøm, Arnab Roy
This paper presents a new efficient hash function for imaginary class groups. Many class group based protocols, such as verifiable delay functions, timed commitments and accumulators, rely on the existence of an efficient and secure hash function, but there are not many concrete constructions available in the literature, and existing constructions are too inefficient for practical use cases.
Our novel approach, building on Wesolowski's initial scheme, achieves a staggering 500-fold increase in computation speed, making it exceptionally practical for real-world applications. This optimisation is achieved at the cost of a smaller image of the hash function, but we show that the image is still sufficiently large for the hash function to be secure. Additionally, our construction is almost linear in its ability to be parallelized, which significantly enhances its computational efficiency on multi-processor systems, making it highly suitable for modern computing environments.
Our novel approach, building on Wesolowski's initial scheme, achieves a staggering 500-fold increase in computation speed, making it exceptionally practical for real-world applications. This optimisation is achieved at the cost of a smaller image of the hash function, but we show that the image is still sufficiently large for the hash function to be secure. Additionally, our construction is almost linear in its ability to be parallelized, which significantly enhances its computational efficiency on multi-processor systems, making it highly suitable for modern computing environments.
Thomas Peters, Yaobin Shen, François-Xavier Standaert
Authenticated Encryption (AE) modes of operation based on Tweakable Block Ciphers (TBC) usually measure efficiency in the number of calls to the underlying primitive per message block. On the one hand, many existing solutions reach a primitive-rate of 1, meaning that each n-bit block of message asymptotically needs a single call to the TBC with output length n. On the other hand, while these modes look optimal in a blackbox setting, they become less attractive when leakage comes into play, since all these calls must then be equally well protected to maintain security. Leakage-resistant modes improve this situation, by generating ephemeral keys every constant number of calls. However, rekeying is inherently suboptimal in primitive-rate, since a TBC call can only be used either to refresh a key or to encrypt a block. Even worse, existing solutions achieving almost n bits of security for n-bit secret keys have at most a primitive-rate 2/3. Hence the question: Can we design a highly-secure TBC-based rekeying mode with ``nearly optimal'' primitive-rate? We answer this question positively with Multiplex, a new mode that has primitive-rate d/(d+1) given a TBC with a dn-bit tweak. Multiplex achieves $n-\log_2(dn)$ bits of security for both (i) misuse-resilience CCA security in the blackbox setting and (ii) Ciphertext Integrity with Misuse-resistant and unbounded Leakage in encryption and decryption (CIML2). It also provides (iii) confidentiality with leakage up to the birthday bound. Furthermore, Multiplex can run d+1 calls in parallel in each iteration. The combination of these features gives a mode of operation that inherits most of the good implementation features and flexibility of a Duplex sponge -- therefore paving the way towards sound comparisons between TBC-based and permutation-based AE.
Yijian Zhang, Jun Zhao, Ziqi Zhu, Junqing Gong, Jie Chen
This paper introduces the notion of registered attribute-based signature (registered ABS). Distinctly different from classical attribute-based signature (ABS), registered ABS allows any user to generate their own public/secret key pair and register it with the system. The key curator is critical to keep the system flowing, which is a fully transparent entity that does not retain secrets. Our results can be summarized as follows.
-This paper provides the first definition of registered ABS, which has never been defined.
-This paper presents the first generic fully secure registered ABS over the prime-order group from $k$-Lin assumption under the standard model, which supports various classes of predicate.
-This paper gives the first concrete registered ABS scheme for arithmetic branching program (ABP), which achieves full security in the standard model.
Technically, our registered ABS is inspired by the blueprint of Okamoto and Takashima[PKC'11]. We convert the prime-order registered attribute-based encryption (registered ABE) scheme of Zhu et al.[ASIACRYPT'23] via predicate encoding to registered ABS by employing the technique of re-randomization with specialized delegation, while we employ the different dual-system method considering the property of registration. Prior to our work, the work of solving the key-escrow issue was presented by Okamoto and Takashima[PKC'13] while their work considered the weak adversary in the random oracle model.
-This paper provides the first definition of registered ABS, which has never been defined.
-This paper presents the first generic fully secure registered ABS over the prime-order group from $k$-Lin assumption under the standard model, which supports various classes of predicate.
-This paper gives the first concrete registered ABS scheme for arithmetic branching program (ABP), which achieves full security in the standard model.
Technically, our registered ABS is inspired by the blueprint of Okamoto and Takashima[PKC'11]. We convert the prime-order registered attribute-based encryption (registered ABE) scheme of Zhu et al.[ASIACRYPT'23] via predicate encoding to registered ABS by employing the technique of re-randomization with specialized delegation, while we employ the different dual-system method considering the property of registration. Prior to our work, the work of solving the key-escrow issue was presented by Okamoto and Takashima[PKC'13] while their work considered the weak adversary in the random oracle model.
Shuhao Zheng, Zonglun Li, Junliang Luo, Ziyue Xin, Xue Liu
Decentralized Anonymous Credential (DAC) systems are increasingly relevant, especially when enhancing revocation mechanisms in the face of complex traceability challenges. This paper introduces IDEA-DAC, a paradigm shift from the conventional revoke-and-reissue methods, promoting direct and Integrity-Driven Editing (IDE) for Accountable DACs, which results in better integrity accountability, traceability, and system simplicity. We further incorporate an Edit-bound Conformity Check that ensures tailored integrity standards during credential amendments using R1CS-based ZK-SNARKs. Delving deeper, we propose ZK-JSON, a unique R1CS circuit design tailored for IDE over generic JSON documents. This design imposes strictly $O(N)$ rank-1 constraints for variable-length JSON documents of up to $N$ bytes in length, encompassing serialization, encryption, and edit-bound conformity checks. Additionally, our circuits only necessitate a one-time compilation, setup, and smart contract deployment for homogeneous JSON documents up to a specified size. While preserving core DAC features such as selective disclosure, anonymity, and predicate provability, IDEA-DAC achieves precise data modification checks without revealing private content, ensuring only authorized edits are permitted. In summary, IDEA-DAC offers an enhanced methodology for large-scale JSON-formatted credential systems, setting a new standard in decentralized identity management efficiency and precision.
Samuel Bouaziz--Ermann, Garazi Muguruza
Pseudorandom Quantum States (PRS) were introduced by Ji, Liu and Song as quantum analogous to Pseudorandom Generators. They are an ensemble of states efficiently computable but computationally indistinguishable from Haar random states. Subsequent works have shown that some cryptographic primitives can be constructed from PRSs. Moreover, recent classical and quantum oracle separations of PRS from One-Way Functions strengthen the interest in a purely quantum alternative building block for quantum cryptography, potentially weaker than OWFs.
However, our lack of knowledge of extending or shrinking the number of qubits of the PRS output still makes it difficult to reproduce some of the classical proof techniques and results. Short-PRSs, that is PRSs with logarithmic size output, have been introduced in the literature along with cryptographic applications, but we still do not know how they relate to PRSs. Here we answer half of the question, by showing that it is not possible to shrink the output of a PRS from polynomial to logarithmic qubit length while still preserving the pseudorandomness property, in a relativized way. More precisely, we show that relative to Kretschmer's quantum oracle (TQC 2021) short-PRSs cannot exist (while PRSs exist, as shown by Kretschmer's work).
However, our lack of knowledge of extending or shrinking the number of qubits of the PRS output still makes it difficult to reproduce some of the classical proof techniques and results. Short-PRSs, that is PRSs with logarithmic size output, have been introduced in the literature along with cryptographic applications, but we still do not know how they relate to PRSs. Here we answer half of the question, by showing that it is not possible to shrink the output of a PRS from polynomial to logarithmic qubit length while still preserving the pseudorandomness property, in a relativized way. More precisely, we show that relative to Kretschmer's quantum oracle (TQC 2021) short-PRSs cannot exist (while PRSs exist, as shown by Kretschmer's work).
Martin Mittelbach, Rafael F. Schaefer, Matthieu Bloch, Aylin Yener, Onur Gunlu
We consider a secure integrated sensing and communication (ISAC) scenario, in which a signal is transmitted through a state-dependent wiretap channel with one legitimate receiver with which the transmitter communicates and one honest-but-curious target that the transmitter wants to sense. The secure ISAC channel is modeled as two state-dependent fast-fading channels with correlated Rayleigh fading coefficients and independent additive Gaussian noise components. Delayed channel outputs are fed back to the transmitter to improve the communication performance and to estimate the channel state sequence. We establish and illustrate an achievable secrecy-distortion region for degraded secure ISAC channels under correlated Rayleigh fading. We also evaluate the inner bound for a large set of parameters to derive practical design insights for secure ISAC methods. The presented results include in particular parameter ranges for which the secrecy capacity of a classical wiretap channel setup is surpassed and for which the channel capacity is approached.
Dilara Toprakhisar, Svetla Nikova, Ventzislav Nikov
Since the first fault attack by Boneh et al. in 1997, various physical fault injection mechanisms have been explored to induce errors in electronic systems. Subsequent fault analysis methods of these errors have been studied, and successfully used to attack many cryptographic implementations. This poses a significant challenge to the secure implementation of cryptographic algorithms. To address this, numerous countermeasures have been proposed. Nevertheless, these countermeasures are primarily designed to protect against the particular assumptions made by the fault analysis methods. These assumptions, however, encompass only a limited range of the capabilities inherent to physical fault injection mechanisms.
In this paper, we narrow our focus to fault attacks and countermeasures specific to ASICs, and introduce a novel parameterized fault adversary model capturing an adversary's control over an ASIC. We systematically map (a) the physical fault injection mechanisms, (b) adversary models assumed in fault analysis, and (c) adversary models used to design countermeasures into our introduced model. This model forms the basis for our comprehensive exploration that covers a broad spectrum of fault attacks and countermeasures within symmetric key cryptography as a comprehensive survey. Furthermore, our investigation highlights a notable misalignment among the adversary models assumed in countermeasures, fault attacks, and the intrinsic capabilities of the physical fault injection mechanisms. Through this study, we emphasize the need to reevaluate existing fault adversary models, and advocate for the development of a unified model.
In this paper, we narrow our focus to fault attacks and countermeasures specific to ASICs, and introduce a novel parameterized fault adversary model capturing an adversary's control over an ASIC. We systematically map (a) the physical fault injection mechanisms, (b) adversary models assumed in fault analysis, and (c) adversary models used to design countermeasures into our introduced model. This model forms the basis for our comprehensive exploration that covers a broad spectrum of fault attacks and countermeasures within symmetric key cryptography as a comprehensive survey. Furthermore, our investigation highlights a notable misalignment among the adversary models assumed in countermeasures, fault attacks, and the intrinsic capabilities of the physical fault injection mechanisms. Through this study, we emphasize the need to reevaluate existing fault adversary models, and advocate for the development of a unified model.
Christina Boura, Nicolas David, Patrick Derbez, Rachelle Heim Boissier, María Naya-Plasencia
Differential cryptanalysis is an old and powerful attack against block ciphers. While different techniques have been introduced throughout the years to improve the complexity of this attack, the key recovery phase remains a tedious and error-prone procedure. In this work, we propose a new algorithm and its associated tool that permits, given a distinguisher, to output an efficient key guessing strategy. Our tool can be applied to SPN ciphers whose linear layer consists of a bit-permutation and whose key schedule is linear or almost linear. It can be used not only to help cryptanalysts find the best differential attack on a given cipher but also to assist designers in their security analysis. We applied our tool to four targets: RECTANGLE, PRESENT-80, SPEEDY-7-192 and GIFT-64. We extend the previous best attack on RECTANGLE-128 by one round and the previous best differential attack against PRESENT-80 by 2 rounds. We improve a previous key recovery step in an attack against SPEEDY and present more efficient key recovery strategies for RECTANGLE-80 and GIFT. Our tool outputs the results in only a second for most targets.
Dilara Toprakhisar, Svetla Nikova, Ventzislav Nikov
Physical attacks pose a substantial threat to the secure implementation of cryptographic algorithms. While considerable research efforts are dedicated to protecting against passive physical attacks (e.g., side-channel analysis (SCA)), the landscape of protection against other types of physical attacks remains a challenge. Fault attacks (FA), though attracting growing attention in research, still lack the prevalence of provably secure designs when compared to SCA. The realm of combined attacks, which leverage the capabilities of both SCA and FA adversaries, introduces powerful adversarial models, rendering protection against them challenging. This challenge has consequently led to a relatively unexplored area of research, resulting in a notable gap in understanding and efficiently protecting against combined attacks. The CAPA countermeasure, published at CRYPTO 2018, addresses this challenge with a robust adversarial model that goes beyond conventional SCA and FA adversarial models. Drawing inspiration from the principles of Multiparty Computation (MPC), CAPA claims security against higher-order SCA, higher-order fault attacks, and their combination. In this work, we present a combined attack that breaks CAPA within the constraints of its assumed adversarial model. In response, we propose potential fixes to the design of CAPA that increase the complexity of the proposed attack, although not provably thwarting it. With this presented combined attack, we highlight the difficulty of effectively protecting against combined attacks.
Jules Maire, Damien Vergnaud
We present a novel technique within the MPC-in-the-Head framework, aiming to design efficient zero-knowledge protocols and digital signature schemes. The technique allows for the simultaneous use of additive and multiplicative sharings of secret information, enabling efficient proofs of linear and multiplicative relations.
The applications of our technique are manifold. It is first applied to construct zero-knowledge arguments of knowledge for Double Discrete Logarithms (DDLP). The resulting protocol achieves improved communication complexity without compromising efficiency. We also propose a new zero-knowledge argument of knowledge for the Permuted Kernel Problem. Eventually, we suggest a short (candidate) post-quantum digital signature scheme constructed from a new one-way function based on simple polynomials known as fewnomials. This scheme offers simplicity and ease of implementation.
Finally, we present two additional results inspired by this work but using alternative approaches. We propose a zero-knowledge argument of knowledge of an RSA plaintext for a small public exponent that significantly improves the state-of-the-art communication complexity.
We also detail a more efficient forward-backward construction for the DDLP.
Paweł Lorek, Moti Yung, Filip Zagórski
Randomized Partial Checking (RPC} was proposed by Jakobsson, Juels, and Rivest and attracted attention as an efficient method of verifying the correctness of the mixing process in numerous applied scenarios. In fact,
RPC is a building block for many electronic voting schemes, including Prêt à Voter, Civitas, Scantegrity II as well as voting-systems used in real-world elections (e.g., in Australia). Mixing is also used in anonymous transfers of cryptocurrencies.
It turned out, however, that a series of works showed, however, subtle issues with analyses behind RPC. First, that the actual security level of the RPC protocol is way off the claimed bounds. The probability of successful manipulation of $k$ votes is $(\frac{3}{4})^k$ instead of the claimed $\frac{1}{2^k}$ (this difference, in turn, negatively affects actual implementations of the notion within existing election systems. This is so since concrete implemented procedures of a given length were directly based on this parameter).
Further, privacy guarantees that a constant number of mix-servers is enough turned out to also not be correct. We can conclude from the above that these analyses of the processes of mixing are not trivial.
In this paper, we review the relevant attacks, and we present Mirrored-RPC -- a fix to RPC based on ``mirrored commitment'' which makes it optimally secure; namely, having a probability of successful manipulation of $k$ votes $\frac{1}{2^k}$.
Then, we present an analysis of the privacy level of both RPC and mRPC. We show that for $n$ messages, the number of mix-servers (rounds) needed to be $\varepsilon$-close to the uniform distribution in total variation distance is lower bounded by: \[ r(n, \varepsilon) \geq \log_{2}{n \choose 2}/\varepsilon. \]
This proof of privacy, in turn, gives insights into the anonymity of various cryptocurrencies (e.g., Zerocash) using anonymizing pools. If a random fraction $q$ of $n$ existing coins is mixed (in each block), then to achieve full anonymity, the number of blocks one needs to run the protocol for, is: \[ rb(n, q, \varepsilon) \geq - \frac{\log n + \log (n-1) - \log (2\varepsilon)}{ {\log({1-q^2}})}. \]
It turned out, however, that a series of works showed, however, subtle issues with analyses behind RPC. First, that the actual security level of the RPC protocol is way off the claimed bounds. The probability of successful manipulation of $k$ votes is $(\frac{3}{4})^k$ instead of the claimed $\frac{1}{2^k}$ (this difference, in turn, negatively affects actual implementations of the notion within existing election systems. This is so since concrete implemented procedures of a given length were directly based on this parameter).
Further, privacy guarantees that a constant number of mix-servers is enough turned out to also not be correct. We can conclude from the above that these analyses of the processes of mixing are not trivial.
In this paper, we review the relevant attacks, and we present Mirrored-RPC -- a fix to RPC based on ``mirrored commitment'' which makes it optimally secure; namely, having a probability of successful manipulation of $k$ votes $\frac{1}{2^k}$.
Then, we present an analysis of the privacy level of both RPC and mRPC. We show that for $n$ messages, the number of mix-servers (rounds) needed to be $\varepsilon$-close to the uniform distribution in total variation distance is lower bounded by: \[ r(n, \varepsilon) \geq \log_{2}{n \choose 2}/\varepsilon. \]
This proof of privacy, in turn, gives insights into the anonymity of various cryptocurrencies (e.g., Zerocash) using anonymizing pools. If a random fraction $q$ of $n$ existing coins is mixed (in each block), then to achieve full anonymity, the number of blocks one needs to run the protocol for, is: \[ rb(n, q, \varepsilon) \geq - \frac{\log n + \log (n-1) - \log (2\varepsilon)}{ {\log({1-q^2}})}. \]
Barış Ege, Bob Swinkels, Dilara Toprakhisar, Praveen Kumar Vadnala
Statistical Fault Attacks (SFA), introduced by Fuhr et al., exploit the statistical bias resulting from injected faults. Unlike prior fault analysis attacks, which require both faulty and correct ciphertexts under the same key, SFA leverages only faulty ciphertexts. In CHES 2018, more powerful attacks called Statistical Ineffective Fault Attacks (SIFA) have been proposed. In contrast to the previous fault attacks that utilize faulty ciphertexts, SIFA exploits the distribution of the intermediate values leading to fault-free ciphertexts. As a result, the SIFA attacks were shown to be effective even in the presence of widely used fault injection countermeasures based on detection and infection. In this work, we build upon the core idea of SIFA, and provide two main practical improvements over the previously proposed analysis methods. Firstly, we show how to perform SIFA from the input side, which in contrast to the original SIFA, requires injecting faults in the earlier rounds of an encryption or decryption operation. If we consider the start of the operation as the trigger for fault injection, the cumulative jitter in the first few rounds of a cipher is much lower than the last rounds. Hence, performing the attack in the first or second round requires a narrower parameter range for fault injection and hence less fault injection attempts to recover the secret key. Secondly, in comparison to the straightforward SIFA approach of guessing 32-bits at a time, we propose a chosen input approach that reduces the guessing effort to 16-bits at a time. This decreases the key search space for full key recovery of an AES-128 implementation from $2^{34}$ to $2^{19}$.
Carmit Hazay, Yibin Yang
A recent work by Ball, Li, Lin, and Liu [Eurocrypt'23] presented a new instantiation of the arithmetic garbling paradigm introduced by Applebaum, Ishai, and Kushilevitz [FOCS'11]. In particular, Ball et al.'s garbling scheme is the first constant-rate garbled circuit over large enough bounded integer computations, inferring the first constant-round constant-rate secure two-party computation (2PC) over bounded integer computations in the presence of semi-honest adversaries.
The main source of difficulty in lifting the security of garbling schemes-based protocols to the malicious setting lies in proving the correctness of the underlying garbling scheme. In this work, we analyze the security of Ball et al.'s scheme in the presence of malicious attacks.
- We demonstrate an overflow attack, which is inevitable in this computational model, even if the garbled circuit is fully correct. Our attack follows by defining an adversary, corrupting either the garbler or the evaluator, that chooses a bad input and causes the computation to overflow, thus leaking information about the honest party's input. By utilizing overflow attacks, we show that $1$-bit leakage is necessary for achieving security against a malicious garbler, discarding the possibility of achieving full malicious security in this model. We further demonstrate a wider range of overflow attacks against a malicious evaluator with more than $1$ bit of leakage.
- We boost the security level of Ball et al.'s scheme by utilizing two variants of Vector Oblivious Linear Evaluation, denoted by VOLEc and aVOLE. We present the first constant-round constant-rate 2PC protocol over bounded integer computations, in the presence of a malicious garbler with $1$-bit leakage and a semi-honest evaluator, in the {VOLEc,aVOLE}-hybrid model and being black-box in the underlying group and ring. Compared to the semi-honest variant, our protocol incurs only a constant factor overhead, both in computation and communication. The constant-round and constant-rate properties hold even in the plain model.
The main source of difficulty in lifting the security of garbling schemes-based protocols to the malicious setting lies in proving the correctness of the underlying garbling scheme. In this work, we analyze the security of Ball et al.'s scheme in the presence of malicious attacks.
- We demonstrate an overflow attack, which is inevitable in this computational model, even if the garbled circuit is fully correct. Our attack follows by defining an adversary, corrupting either the garbler or the evaluator, that chooses a bad input and causes the computation to overflow, thus leaking information about the honest party's input. By utilizing overflow attacks, we show that $1$-bit leakage is necessary for achieving security against a malicious garbler, discarding the possibility of achieving full malicious security in this model. We further demonstrate a wider range of overflow attacks against a malicious evaluator with more than $1$ bit of leakage.
- We boost the security level of Ball et al.'s scheme by utilizing two variants of Vector Oblivious Linear Evaluation, denoted by VOLEc and aVOLE. We present the first constant-round constant-rate 2PC protocol over bounded integer computations, in the presence of a malicious garbler with $1$-bit leakage and a semi-honest evaluator, in the {VOLEc,aVOLE}-hybrid model and being black-box in the underlying group and ring. Compared to the semi-honest variant, our protocol incurs only a constant factor overhead, both in computation and communication. The constant-round and constant-rate properties hold even in the plain model.
Antoine Joux, Hunter Kippen, Julian Loss
Since its introduction by Wagner (CRYPTO `02), the $k$-list algorithm has found significant utility in cryptanalysis. One important application thereof is in computing forgeries on several interactive signature schemes that implicitly rely on the hardness of the ROS problem formulated by Schnorr (ICICS `01). The current best attack strategy for these schemes relies the conjectured runtime of the $k$-list algorithm over $\mathbb{Z}_p$. The tightest known analysis of Wagner's algorithm over $\mathbb{Z}_p$ is due to Shallue (ANTS `08). However, it hides large polynomial factors and leaves a gap with respect to desirable concrete parameters for the attack. In this work, we develop a degraded version of the $k$-list algorithm which provably enforces the heuristic invariants in Wagner's original. In the process, we devise and analyze a new list merge procedure that we dub the interval merge. We give a thorough analysis of the runtime and success probability of our degraded algorithm, and show that it beats the projected runtime of the analysis by Shallue for parameters relevant to the generalized ROS attack of Benhamouda et al. (EUROCRYPT `21). For a $256$-bit prime $p$, and $k = 8$, our degraded $k$-list algorithm runs in time $\approx 2^{70.4}$, while Shallue's analysis states that the Wagner's original algorithm runs in time $\approx 2^{98.3}$.
Polynomial Commitments from Lattices: Post-Quantum Security, Fast Verification and Transparent Setup
Valerio Cini, Giulio Malavolta, Ngoc Khanh Nguyen, Hoeteck Wee
Polynomial commitment scheme allows a prover to commit to a polynomial $f \in \mathcal{R}[X]$ of degree $L$, and later prove that the committed function was correctly evaluated at a specified point $x$; in other words $f(x)=u$ for public $x,u \in\mathcal{R}$. Most applications of polynomial commitments, e.g. succinct non-interactive arguments of knowledge (SNARKs), require that (i) both the commitment and evaluation proof are succinct (i.e., polylogarithmic in the degree $L$) - with the latter being efficiently verifiable, and (ii) no pre-processing step is allowed.
Surprisingly, as far as plausibly quantum-safe polynomial commitments are concerned, the currently most efficient constructions only rely on weak cryptographic assumptions, such as security of hash functions. Indeed, despite making use of the underlying algebraic structure, prior lattice-based polynomial commitments still seem to be much behind the hash-based ones. Moreover, security of the aforementioned lattice constructions against quantum adversaries was never formally discussed.
In this work, we bridge the gap and propose the first (asymptotically and concretely) efficient lattice-based polynomial commitment with transparent setup and post-quantum security. Our interactive variant relies on the standard (Module-)SIS problem, and can be made non-interactive in the random oracle model using Fiat-Shamir transformation. In addition, we equip the scheme with a knowledge soundness proof against quantum adversaries which can be of independent interest. In terms of concrete efficiency, for $L=2^{20}$ our scheme yields proofs of size $2$X smaller than the hash-based \textsf{FRI} commitment (Block et al., Asiacrypt 2023), and $70$X smaller than the very recent lattice-based construction by Albrecht et al. (Eurocrypt 2024).
Surprisingly, as far as plausibly quantum-safe polynomial commitments are concerned, the currently most efficient constructions only rely on weak cryptographic assumptions, such as security of hash functions. Indeed, despite making use of the underlying algebraic structure, prior lattice-based polynomial commitments still seem to be much behind the hash-based ones. Moreover, security of the aforementioned lattice constructions against quantum adversaries was never formally discussed.
In this work, we bridge the gap and propose the first (asymptotically and concretely) efficient lattice-based polynomial commitment with transparent setup and post-quantum security. Our interactive variant relies on the standard (Module-)SIS problem, and can be made non-interactive in the random oracle model using Fiat-Shamir transformation. In addition, we equip the scheme with a knowledge soundness proof against quantum adversaries which can be of independent interest. In terms of concrete efficiency, for $L=2^{20}$ our scheme yields proofs of size $2$X smaller than the hash-based \textsf{FRI} commitment (Block et al., Asiacrypt 2023), and $70$X smaller than the very recent lattice-based construction by Albrecht et al. (Eurocrypt 2024).