International Association
for Cryptologic Research

In differential-like attacks, the process typically involves extending a distinguisher forward and backward with probability 1 for some rounds and recovering the key involved in the extended part. Particularly in rectangle attacks, a holistic key recovery strategy can be employed to yield the most efficient attacks tailored to a given distinguisher. In this paper, we treat the distinguisher and the extended part as an integrated entity and give a one-step framework for finding rectangle attacks with the purpose of reducing the overall complexity or attacking more rounds. In this framework, we propose to allow probabilistic differential propagations in the extended part and incorporate the holistic recovery strategy. Additionally, we introduce the ``split-and-bunch technique'' to further reduce the time complexity. Beyond rectangle attacks, we extend these foundational concepts to encompass differential attacks as well. To demonstrate the efficiency of our framework, we apply it to Deoxys-BC-384, SKINNY, ForkSkinny, and CRAFT, achieving a series of refined and improved rectangle attacks and differential attacks. Notably, we obtain the first 15-round attack on Deoxys-BC-384, narrowing its security margin to only one round. Furthermore, our differential attack on CRAFT extends to 23 rounds, covering two more rounds than the previous best attacks.

Number Theoretic Transform (NTT) has been widely used in accelerating computations in lattice-based cryptography. However, attackers can potentially launch power analysis targeting the NTT because it is one of the most time-consuming parts of the implementation. This extended time frame provides a natural window of opportunity for attackers. In this paper, we investigate the first CPU frequency leakage (Hertzbleed-like) attacks against NTT in lattice-based KEMs. Our key observation is that different inputs to NTT incur different Hamming weights in its output and intermediate layers. By measuring the CPU frequency during the execution of NTT, we propose a simple yet effective attack idea to find the input to NTT that triggers NTT processing data with significantly low Hamming weight. We further apply our attack idea to real-world applications that are built upon NTT: CPAsecure Kyber without Compression and Decompression functions, and CCA-secure NTTRU. This leads us to extract information or frequency hints about the secret key. Integrating these hints into the LWE-estimator framework, we estimate a minimum of 35% security loss caused by the leakage. The frequency and timing measurements on the Reference and AVX2 implementations of NTT in both Kyber and NTTRU align well with our theoretical analysis, confirming the existence of frequency side-channel leakage in NTT. It is important to emphasize that our observation is not limited to a specific implementation but rather the algorithm on which NTT is based. Therefore, our results call for more attention to the analysis of power leakage against NTT in lattice-based cryptography.

In these years, many messaging platforms have integrated end-to-end (E2E) encryption into their services. This widespread adoption of E2E encryption has triggered a technical tension between user privacy and illegal content moderation. The existing solutions either support only unframeability or deniability, or they are prone to abuse (the moderator can perform content moderation for all messages, whether illegal or not), or they lack mechanisms for retrospective content moderation. To address the above issues, we introduce a new primitive called \emph{mild asymmetric message franking} (MAMF) to establish illegal-messages-only and retrospective content moderation for messaging systems, supporting unframeability and deniability simultaneously. We provide a framework to construct MAMF, leveraging two new building blocks, which might be of independent interest.

At Asiacrypt 2022, a holistic key guessing strategy was proposed to yield the most efficient key recovery for the rectangle attack. Recently, at Crypto 2023, a new cryptanalysis technique--the differential meet-in-the-middle (MITM) attack--was introduced. Inspired by these two previous works, we present three generic key recovery attacks in this paper. First, we extend the holistic key guessing strategy from the rectangle to the differential attack, proposing the generic classical differential attack (GCDA). Next, we combine the holistic key guessing strategy with the differential MITM attack, resulting in the generalized differential MITM attack (GDMA). Finally, we apply the MITM technique to the rectangle attack, creating the generic rectangle MITM attack (GRMA). In terms of applications, we improve 12/13-round attacks on AES-256. For 12-round AES-256, by using the GDMA, we reduce the time complexity by a factor of 2^{62}; by employing the GCDA, we reduce both the time and memory complexities by factors of 2^{61} and 2^{56}, respectively. For 13-round AES-256, we present a new differential attack with data and time complexities of 2^{89} and 2^{240}, where the data complexity is 2^{37} times lower than previously published results. These are currently the best attacks on AES-256 using only two related keys. For KATAN-32, we increase the number of rounds covered by the differential attack from 115 to 151 in the single-key setting using the basic differential MITM attack (BDMA) and GDMA. Furthermore, we achieve the first 38-round rectangle attack on SKINNYe-64-256 v2 by using the GRMA.

<p> The Learning with Errors (LWE) problem has become one of the most prominent candidates of post-quantum cryptography, offering promising potential to meet the challenge of quantum computing. From a theoretical perspective, optimizing algorithms to solve LWE is a vital task for the analysis of this cryptographic primitive. In this paper, we propose a fine-grained time/memory trade-off method to analyze c-sum BKW variants for LWE in both classical and quantum models, then offer new complexity bounds for multiple BKW variants determined by modulus q, dimension k, error rate alpha, and stripe size b. Through our analysis, optimal parameters can be efficiently found for different settings, and the minimized complexities are lower than existing results. Furthermore, we enhance the performance of c-sum BKW in the quantum computing model by adopting the quantum Meet-in-the-Middle technique as c-sum solver instead of the naive c-sum technique. Our complexity trade-off formula also applies to the quantum version of BKW, and optimizes the theoretical quantum time and memory costs, which are exponentially lower than existing quantum c-sum BKW variants. </p>

As online group communication scenarios become more and more common these years, malicious or unpleasant messages are much easier to spread on the internet. Message franking is a crucial cryptographic mechanism designed for content moderation in online end-to-end messaging systems, allowing the receiver of a malicious message to report the message to the moderator. Unfortunately, the existing message franking schemes only consider 1-1 communication scenarios. In this paper, we systematically explore message franking in group communication scenarios. We introduce the notion of asymmetric group message franking (AGMF), and formalize its security requirements. Then, we provide a framework of constructing AGMF from a new primitive, called $\textup{HPS-KEM}^{\rm{\Sigma}}$. We also give a construction of $\textup{HPS-KEM}^{\rm{\Sigma}}$ based on the DDH assumption. Plugging the concrete $\textup{HPS-KEM}^{\rm{\Sigma}}$ scheme into our AGMF framework, we obtain a DDH-based AGMF scheme, which supports message franking in group communication scenarios.

Protocols with \emph{publicly verifiable covert (PVC) security} offer high efficiency and an appealing feature: a covert party may deviate from the protocol, but with a probability (e.g., $90\%$, referred to as the \emph{deterrence factor}), the honest party can identify this deviation and expose it using a publicly verifiable certificate. These protocols are particularly suitable for practical applications involving reputation-conscious parties. However, in the cases where misbehavior goes undetected (e.g., with a probability of $10\%$), \emph{no security guarantee is provided for the honest party}, potentially resulting in a complete loss of input privacy and output correctness. In this paper, we tackle this critical problem by presenting a highly effective solution. We introduce and formally define an enhanced notion called \emph{robust PVC security}, such that even if the misbehavior remains undetected, the malicious party can only gain an additional $1$-bit of information about the honest party's input while maintaining the correctness of the output. We propose a novel approach leveraging \emph{dual execution} and \emph{time-lock puzzles} to design a robust PVC-secure two-party protocol with \emph{low overhead} (depending on the deterrence factor). For instance, with a deterrence factor of $90\%$, our robust PVC-secure protocol incurs \emph{only additional ${\sim}10\%$ overhead} compared to the state-of-the-art PVC-secure protocol. Given the stronger security guarantees with low overhead, our protocol is highly suitable for practical applications of secure two-party computation.

In this paper, we consider to generalize NIZK by empowering a prover to share a witness in a fine-grained manner with verifiers. Roughly, the prover is able to authorize a verifier to obtain extra information of witness, i.e., besides verifying the truth of the statement, the verifier can additionally obtain certain function of the witness from the accepting proof using a secret key provided by the prover. To fulfill these requirements, we introduce a new primitive called \emph{non-interactive zero-knowledge functional proofs (fNIZKs)}, and formalize its security notions. We provide a generic construction of fNIZK for any $\NP$ relation $\R$, which enables the prover to share any function of the witness with a verifier. For a widely-used relation about set membership proof (implying range proof), we construct a concrete and efficient fNIZK, through new building blocks (set membership encryption and dual inner-product encryption), which might be of independent interest.

The rectangle attack has shown to be a very powerful form of cryptanalysis against block ciphers. Given a rectangle distinguisher, one expects to mount key recovery attacks as efficiently as possible. In the literature, there have been four algorithms for rectangle key recovery attacks. However, their performance vary from case to case. Besides, numerous are the applications where the attacks lack optimality. In this paper, we investigate the rectangle key recovery in depth and propose a unified and generic key recovery algorithm, which supports any possible attacking parameters. Notably, it not only covers the four previous rectangle key recovery algorithms, but also unveils five types of new attacks which were missed previously. Along with the new key recovery algorithm, we propose a framework for automatically finding the best attacking parameters, with which the time complexity of the rectangle attack will be minimized using the new algorithm. To demonstrate the efficiency of the new key recovery algorithm, we apply it to Serpent, CRAFT, SKINNY and Deoxys-BC-256 based on existing distinguishers and obtain a series of improved rectangle attacks.

Anonymity of public key encryption (PKE) requires that, in a multi-user scenario, the PKE ciphertexts do not leak information about which public keys are used to generate them. Corruptions are common threats in the multi-user scenario but anonymity of PKE under corruptions is less studied in the literature. In TCC 2020, Benhamouda et al. first provide a formal characterization for anonymity of PKE under a specific type of corruption. However, no known PKE scheme is proved to meet their characterization. To the best of our knowledge, all the PKE application scenarios which require anonymity also require confidentiality. However, in the work by Benhamouda et al., different types of corruptions for anonymity and confidentiality are considered, which can cause security pitfalls. What's worse, we are not aware of any PKE scheme which can provide both anonymity and confidentiality under the same types of corruptions. In this work, we introduce a new security notion for PKE called ANON-RSO$_{k}\&$C security, capturing anonymity under corruptions. We also introduce SIM-RSO$_{k}\&$C security which captures confidentiality under the same types of corruptions. We provide a generic framework of constructing PKE scheme which can achieve the above two security goals simultaneously based on a new primitive called key and message non-committing encryption (KM-NCE). Then we give a general construction of KM-NCE utilizing a variant of hash proof system (HPS) called Key-Openable HPS. We also provide Key-Openable HPS instantiations based on the matrix decisional Diffie-Hellman assumption. Therefore, we can obtain various concrete PKE instantiations achieving the two security goals in the standard model with \emph{compact} ciphertexts. Furthermore, for some PKE instantiation, its security reduction is \emph{tight}.

In this work, we propose the first identity-based matchmaking encryption (IB-ME) scheme under the standard assumptions in the standard model. This scheme is proven to be secure under the symmetric external Diffie-Hellman (SXDH) assumption in prime order bilinear pairing groups. In our IB-ME scheme, all parameters have constant number of group elements and are simpler than those of previous constructions. Previous works are either in the random oracle model or based on the q-type assumptions, while ours is built directly in the standard model and based on static assumptions, and does not rely on other crypto tools. More concretely, our IB-ME scheme is constructed from a variant of two-level anonymous IBE. We observed that this two-level IBE with anonymity and unforgeability satisfies the same functionality of IB-ME, and its security properties cleverly meet the two requirements of IB-ME (Privacy and Authenticity). The privacy property of IB-ME relies on the anonymity of this two-level IBE, while the authenticity property is corresponding to the unforgeability in the 2nd level. This variant of two-level IBE is built from dual pairing vector spaces, and both security reductions rely on dual system encryption.

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

Selective opening attacks (SOA) (for public-key encryption, PKE) concern such a multi-user scenario, where an adversary adaptively corrupts some fraction of the users to break into a subset of honestly created ciphertexts, and tries to learn the information on the messages of some unopened (but potentially related) ciphertexts. Until now, the notion of selective opening attacks is only considered in two settings: sender selective opening (SSO), where part of senders are corrupted and messages together with randomness for encryption are revealed; and receiver selective opening (RSO), where part of receivers are corrupted and messages together with secret keys for decryption are revealed. In this paper, we consider a more natural and general setting for selective opening security. In the setting, the adversary may adaptively corrupt part of senders and receivers \emph{simultaneously}, and get the plaintext messages together with internal randomness for encryption and secret keys for decryption, while it is hoped that messages of uncorrupted parties remain protected. We denote it as Bi-SO security since it is reminiscent of Bi-Deniability for PKE. We first formalize the requirement of Bi-SO security by the simulation-based (SIM) style, and prove that some practical PKE schemes achieve SIM-Bi-$\text{SO}$-CCA security in the random oracle model. Then, we suggest a weak model of Bi-SO security, denoted as SIM-wBi-$\text{SO}$-CCA security, and argue that it is still meaningful and useful. We propose a generic construction of PKE schemes that achieve SIM-wBi-$\text{SO}$-CCA security in the standard model and instantiate them from various standard assumptions. Our generic construction is built on a newly presented primitive, namely, universal$_{\kappa}$ hash proof system with key equivocability, which may be of independent interest.

We propose a generic construction of 2-pass authenticated key exchange (AKE) scheme with explicit authentication from key encapsulation mechanism (KEM) and signature (SIG) schemes. We improve the security model due to Gjosteen and Jager [Crypto2018] to a stronger one. In the strong model, if a replayed message is accepted by some user, the authentication of AKE is broken. We define a new security notion named ''IND-mCPA with adaptive reveals'' for KEM. When the underlying KEM has such a security and SIG has unforgeability with adaptive corruptions, our construction of AKE equipped with counters as states is secure in the strong model, and stateless AKE without counter is secure in the traditional model. We also present a KEM possessing tight ''IND-mCPA security with adaptive reveals'' from the Computation Diffie-Hellman assumption in the random oracle model. When the generic construction of AKE is instantiated with the KEM and the available SIG by Gjosteen and Jager [Crypto2018], we obtain the first practical 2-pass AKE with tight security and explicit authentication. In addition, the integration of the tightly IND-mCCA secure KEM (derived from PKE by Han et al. [Crypto2019]) and the tightly secure SIG by Bader et al. [TCC2015] results in the first tightly secure 2-pass AKE with explicit authentication in the standard model.

The Learning Parity with Noise (LPN) problem has recently found many cryptographic applications such as authentication protocols, pseudorandom generators/functions and even asymmetric tasks including public-key encryption (PKE) schemes and oblivious transfer (OT) protocols. It however remains a long-standing open problem whether LPN implies collision resistant hash (CRH) functions. Inspired by the recent work of Applebaum et al. (ITCS 2017), we introduce a general construction of CRH from LPN for various parameter choices. We show that, just to mention a few notable ones, under any of the following hardness assumptions (for the two most common variants of LPN) 1.constant-noise LPN is $$2^{n^{0.5+\varepsilon }}$$-hard for any constant $$\varepsilon >0$$;2.constant-noise LPN is $$2^{\varOmega (n/\log n)}$$-hard given $$q=\mathsf {poly}(n)$$ samples;3.low-noise LPN (of noise rate $$1/\sqrt{n}$$) is $$2^{\varOmega (\sqrt{n}/\log n)}$$-hard given $$q=\mathsf {poly}(n)$$ samples. there exists CRH functions with constant (or even poly-logarithmic) shrinkage, which can be implemented using polynomial-size depth-3 circuits with NOT, (unbounded fan-in) AND and XOR gates. Our technical route LPN $$\rightarrow $$ bSVP $$\rightarrow $$ CRH is reminiscent of the known reductions for the large-modulus analogue, i.e., LWE $$\rightarrow $$ SIS $$\rightarrow $$ CRH, where the binary Shortest Vector Problem (bSVP) was recently introduced by Applebaum et al. (ITCS 2017) that enables CRH in a similar manner to Ajtai’s CRH functions based on the Short Integer Solution (SIS) problem.Furthermore, under additional (arguably minimal) idealized assumptions such as small-domain random functions or random permutations (that trivially imply collision resistance), we still salvage a simple and elegant collision-resistance-preserving domain extender combining the best of the two worlds, namely, maximized (depth one) parallelizability and polynomial shrinkage. In particular, assume $$2^{n^{0.5+\varepsilon }}$$-hard constant-noise LPN or $$2^{n^{0.25+\varepsilon }}$$-hard low-noise LPN, we obtain a collision resistant hash function that evaluates in parallel only a single layer of small-domain random functions (or random permutations) and shrinks polynomially.