International Association
for Cryptologic Research

Machine Learning (ML) is almost ubiquitously used in multiple disciplines nowadays. Recently, we have seen its usage in the realm of differential distinguishers for symmetric key ciphers. In this work, we explore the possibility of a number of ciphers with respect to various ML-based distinguishers.

We show new distinguishers on the unkeyed and round reduced version of SPECK-32, SPECK-128, ASCON, SIMECK-32, SIMECK-64 and SKINNY-128. We explore multiple avenues in the process. In summary, we use neural network as well as support vector machine in various settings (such as varying the activation function), apart from experimenting with a number of input difference tuples. Among other results, we show a distinguisher of 8-round SPECK-32 that works with practical data complexity (most of the experiments take a few hours on a personal computer).

A private puncturable pseudorandom function (PRF) enables one to create a constrained version of a PRF key, which can be used to evaluate the PRF at all but some punctured points. In addition, the constrained key reveals no information about the punctured points and the PRF values on them. Existing constructions of private puncturable PRFs are only proven to be secure against a restricted adversary that must commit to the punctured points before viewing any information. It is an open problem to achieve the more natural adaptive security, where the adversary can make all its choices on-the-fly.

In this work, we solve the problem by constructing an adaptively secure private puncturable PRF from standard lattice assumptions. To achieve this goal, we present a new primitive called explainable hash, which allows one to reprogram the hash function on a given input. The new primitive may find further applications in constructing more cryptographic schemes with adaptive security. Besides, our construction has collusion resistant pseudorandomness, which requires that even given multiple constrained keys, no one could learn the values of the PRF at the punctured points. Private puncturable PRFs with collusion resistant pseudorandomness were only known from multilinear maps or indistinguishability obfuscations in previous works, and we provide the first solution from standard lattice assumptions.

Unconditionally secure broadcast is feasible among parties connected by pairwise secure links only if there is a strict two-thirds majority of honest parties when no additional resources are available. This limitation may be circumvented when the parties have recourse to additional resources such as correlated randomness. Fitzi, Wolf, and Wullschleger (CRYPTO 2004) attempted to characterize the conditions on correlated randomness shared among three parties which would enable them to realize broadcast. Due to a gap in their impossibility argument, it turns out that their characterization is incorrect. Using a novel construction we show that broadcast is feasible under a considerably larger class of correlations. In fact, we realize pseudo-signatures, which are information theoretic counterparts of digital signatures using which unconditionally secure broadcast may be obtained. We also obtain a matching impossibility result thereby characterizing the class of correlations on which three-party broadcast (and pseudo-signatures) can be based. Our impossibility proof, which extends the well-know argument of Fischer, Lynch and Merritt (Distr. Comp., 1986) to the case where parties observe correlated randomness, maybe of independent interest.

Partially Oblivious Pseudorandom Functions (POPRFs) are 2-party protocols that allow a client to learn pseudorandom function (PRF) evaluations on inputs of its choice from a server. The client submits two inputs, one public and one private. The security properties ensure that the server cannot learn the private input and the client cannot learn more than one evaluation per POPRF query. POPRFs have many applications including password-based key exchange and privacy-preserving authentication mechanisms. However, most constructions are based on classical assumptions and those with post-quantum security suffer from large efficiency drawbacks.

In this work, we construct a novel POPRF from lattice assumptions and the "Crypto Dark Matter" PRF candidate (TCC'18) in the random oracle model. At a conceptual level, our scheme exploits the alignment of this family of PRF candidates, relying on mixed modulus computations, and programmable bootstrapping in the "3rd gen" torus-fully homomorphic encryption scheme (TFHE). We show that our construction achieves malicious client security based on circuit-private FHE, and client privacy from the semantic security of the FHE scheme. We further explore a heuristic approach to extend our scheme to support verifiability based on the difficulty of computing cheating circuits in low depth. This would yield a verifiable (P)OPRF. We provide a proof-of-concept implementation and benchmarks of our construction using the "Concrete" TFHE software library. For the core online OPRF functionality, client operations take only a few milliseconds, while server evaluation takes less than 3 seconds.

Homomorphic Encryption~(HE) is used in many fields including information storage, data protection, privacy preservation, blockchain, and authentication. HE allows an untrusted third party to perform algebraic operations on encrypted data. Protecting the results of HE against accidental or malicious tampering attacks is still an open research challenge. In this paper, we introduce a lightweight technique that allows a data owner to verify the integrity of HE results performed in the cloud. The proposed method is quick, simple, and applicable, as it depends on adding a single digit to the encrypted message before storing it in the cloud. This digit represents verification proof and it is later used to ensure a verifiable HE. Our technique can be integrated with any HE scheme that uses encryption with non-isolated plaintext.

Encrypting too much data using the same key is a bad practice from a security perspective. Hence, it is customary to perform re-keying after a given amount of data is transmitted. While in many cases, the re-keying is done using a fresh execution of some key exchange protocol (e.g., in IKE or TLS), there are scenarios where internal re-keying, i.e., without exchange of information, is performed, mostly due to performance reasons. Originally suggested by Abdalla and Bellare, there are several proposals on how to perform this internal re-keying mechanism. For example, Liliya et al. offered the CryptoPro Key Meshing (CPKM) to be used together with GOST 28147-89 (known as the GOST block cipher). Later, ISO and the IETF adopted the Advanced CryptoPro Key Meshing (ACKPM) in ISO 10116 and RFC 8645, respectively. In this paper, we study the security of ACPKM and CPKM. We show that the internal re-keying suffers from an entropy loss in successive repetitions of the re- keying mechanism. We show some attacks based on this issue. The most prominent one has time and data complexities of $O(2^{\kappa/2} )$ and success rate of $O(2^{−\kappa/4} )$ for a $\kappa$-bit key. Furthermore, we show that a malicious block cipher designer or a faulty implementation can exploit the ACPKM (or the original CPKM) mechanism to significantly hinder the security of a protocol employing ACPKM (or CPKM). Namely, we show that in such cases, the entropy of the re-keyed key can be greatly reduced.

The no-cloning principle of quantum mechanics enables us to achieve amazing unclonable cryptographic primitives, which is impossible in classical cryptography. However, the security definitions for unclonable cryptography are tricky. Achieving desirable security notions for unclonability is a challenging task. In particular, there is no indistinguishable-secure unclonable encryption and quantum copy-protection for single-bit output point functions in the standard model. To tackle this problem, we introduce and study relaxed but meaningful security notions for unclonable cryptography in this work. We call the new security notion one-out-of-many unclonable security.

We obtain the following results. - We show that one-time strong anti-piracy secure secret key single-decryptor encryption (SDE) implies one-out-of-many indistinguishable-secure unclonable encryption. - We construct a one-time strong anti-piracy secure secret key SDE scheme in the standard model from the LWE assumption. - We construct one-out-of-many copy-protection for single-bit output point functions from one-out-of-many indistinguishable-secure unclonable encryption and the LWE assumption. - We construct one-out-of-many unclonable predicate encryption (PE) from one-out-of-many indistinguishable-secure unclonable encryption and the LWE assumption.

Thus, we obtain one-out-of-many indistinguishable-secure unclonable encryption, one-out-of-many copy-protection for single-bit output point functions, and one-out-of-many unclonable PE in the standard model from the LWE assumption. In addition, our one-time SDE scheme is the first SDE scheme that does not rely on any oracle heuristics and strong assumptions such as indistinguishability obfuscation and witness encryption.

Current messaging protocols are incapable of detecting active man-in-the-middle threats. Even common continuous key agreement protocols such as Signal, which offers forward secrecy and post-compromise security, are dependent on the adversary being passive immediately following state compromise, and healing guarantees are lost if the attacker is not. This work offers the first solution for detecting active man-in-the-middle attacks on such protocols by extending authentication beyond the initial public keys and binding it to the entire continuous key agreement. In this, any adversarial fork is identifiable to the protocol participants. We provide a modular construction generic for application with any continuous key agreement protocol, a specific construction for application to Signal, and security analysis. The modularity of our solution enables it to be seamlessly adopted by any continuous key agreement protocol.

The Mixed Integer Linear Programming (MILP) is a common method of searching for impossible differentials (IDs). However, the optimality of the distinguisher should be confirmed by an exhaustive search of all input and output differences, which is clearly computationally infeasible due to the huge search space.

In this paper, we propose a new technique that uses two-dimensional binary variables to model the input and output differences and characterize contradictions with constraints. In our model, the existence of IDs can be directly obtained by checking whether the model has a solution. In addition, our tool can also detect any contradictions between input and output differences by changing the position of the contradictions. Our method is confirmed by applying it to several block ciphers, and our results show that we can find 6-, 13-, and 12-round IDs for Midori-64, CRAFT, and SKINNY-64 within a few seconds, respectively. Moreover, by carefully analyzing the key schedule of Midori-64, we propose an equivalent key transform technique and construct a complete MILP model for an 11-round impossible differential attack (IDA) on Midori-64 to search for the minimum number of keys to be guessed. Based on our automatic technique, we present a new 11-round IDA on Midori-64, where 23 nibbles of keys need to be guessed, which reduces the time complexity compared to previous work. The time and data complexity of our attack are $2^{116.59}$ and $2^{60}$, respectively. To the best of our knowledge, this is the best IDA on Midori-64 at present.

Virtually all modern blockciphers are iterated. In this paper, we ask: to construct a secure iterated blockcipher "non-trivially", how many calls to random functions and permutations are necessary?

When security means indistinguishability from a random permutation, optimality is achieved by the Even-Mansour scheme using 1 call to a public permutation. We seek for the arguably strongest security indifferentiability from an ideal cipher, a notion introduced by Maurer et al. (TCC 2004) and popularized by Coron et al. (JoC, 2014).

We provide the first generic negative result/lower bounds: when the key is not too short, no iterated blockcipher making 3 calls is (statistically) indifferentiable. This proves optimality for a 4-call positive result of Guo et al. (Eprint 2016). Furthermore, using 1 or 2 calls, even indifferentiable iterated blockciphers with polynomial keyspace are impossible.

To prove this, we develop an abstraction of idealized iterated blockciphers and establish various basic properties, and apply Extremal Graph Theory results to prove the existence of certain (generalized) non-random properties such as the boomerang and yoyo.

An oblivious pseudorandom function, or OPRF, is an important primitive that is used to build many advanced cryptographic protocols. Despite its relevance, very few post-quantum solutions exist.

In this work, we propose a novel OPRF protocol that is post-quantum, verifiable, round-optimal, and moderately compact. Our protocol is based on a previous SIDH-based construction by Boneh, Kogan, and Woo, which was later shown to be insecure due to an attack on its one-more unpredictability. We first propose an efficient countermeasure against this attack by redefining the PRF function to use irrational isogenies. This prevents a malicious user from independently evaluating the PRF. The SIDH-based construction by Boneh, Kogan, and Woo is also vulnerable to the recent attacks on SIDH. We thus demonstrate how to efficiently incorporate the countermeasures against such attacks to obtain a secure OPRF protocol. To achieve this, we also propose the first proof of isogeny knowledge that is compatible with masked torsion points, which may be of independent interest. Lastly, we design a novel non-interactive proof of knowledge of parallel isogenies, which reduces the number of communication rounds of the OPRF to the theoretically-optimal two. Putting everything together, we obtain the most compact post-quantum verifiable OPRF protocol.

Falcon is one of the three post-quantum signature schemes selected for standardization by NIST. Due to its low bandwidth and high efficiency, Falcon is seen as an attractive option for quantum-safe embedded systems. In this work, we study Falcon's side-channel resistance by analysing its Gaussian samplers. Our results are mainly twofold.

The first result is an improved key recovery exploiting the leakage within the base sampler investigated by Guerreau et al. (CHES 2022). Instead of resorting to the fourth moment as in former parallelepiped-learning attacks, we work with the second order statistics covariance and use its spectral decomposition to recover the secret information. Our approach substantially reduces the requirement for measurements and computation resources: $220\,000$ traces is sufficient to recover the secret key of Falcon 512 within half an hour with a probability of $\approx 25\%$. As a comparison, even with $10^6$ traces, the former attack still needs about 1000 hours CPU time of lattice reduction for a full key recovery. In addition, our approach is robust to inaccurate leakage classification, which is another advantage over parallelepiped-learning attacks.

Our second result is a practical power analysis targeting the integer Gaussian sampler of Falcon. The analysis relies on the leakage of random sign flip within the integer Gaussian sampling. This leakage was exposed in 2018 by Kim and Hong, but it is not considered in Falcon's implementation and unexploited for side channel analysis until now. We identify the leakage within the reference implementation of Falcon on an ARM Cortex-M4 STM32F407IGT6 microprocessor. We also show that this single bit of leakage is in effect enough for practical key recovery: with $170\,000$ traces one can fully recover the key of Falcon-512 within half an hour. Furthermore, combining the sign leakage and the aforementioned leakage, one can recover the key with only $45\,000$ signature measurements in a short time.

As a by-product, we also extend our power analysis to Mitaka which is a recent variant of Falcon. The same leakages exist within the integer Gaussian samplers of Mitaka, and they can also be used to mount key recovery attacks. Nevertheless, the key recovery in Mitaka requires much more traces than it does in Falcon, due to their different lattice Gaussian samplers.

Verifiable random functions (VRFs) are essentially pseudorandom functions for which selected outputs can be proved correct and unique, without compromising the security of other outputs. VRFs have numerous applications across cryptography, and in particular they have recently been used to implement committee selection in the Algorand protocol.

Elliptic Curve VRF (ECVRF) is an elegant construction, originally due to Papadopoulos et al., that is now under consideration by the Internet Research Task Force. Prior work proved that ECVRF possesses the main desired security properties of a VRF, under suitable assumptions. However, several recent versions of ECVRF include changes that make some of these proofs inapplicable. Moreover, the prior analysis holds only for *classical* attackers, in the random-oracle model (ROM); it says nothing about whether any of the desired properties hold against *quantum* attacks, in the quantumly accessible ROM. We note that certain important properties of ECVRF, like uniqueness, do *not* rely on assumptions that are known to be broken by quantum computers, so it is plausible that these properties could hold even in the quantum setting.

This work provides a multi-faceted security analysis of recent versions of ECVRF, in both the classical and quantum settings. First, we motivate and formally define new security properties for VRFs, like non-malleability and binding, and prove that recent versions of ECVRF satisfy them (under standard assumptions). Second, we identify a subtle obstruction in proving that recent versions of ECVRF have *uniqueness* via prior indifferentiability definitions and theorems, even in the classical setting. Third, we fill this gap by defining a stronger notion called *relative indifferentiability*, and extend prior work to show that a standard domain extender used in ECVRF satisfies this notion, in both the classical and quantum settings. This final contribution is of independent interest and we believe it should be applicable elsewhere.

In this work we present a lightweight lattice-based identification protocol based on the CPA-secured public key encryption scheme Kyber. It is designed as a replacement for existing classical ECC- or RSA-based identification protocols in IoT, smart card applications, or for device authentication. The proposed protocol is simple, efficient, and implementations are supposed to be easy to harden against side-channel attacks. Compared to standard constructions for identification protocols based on lattice-based KEMs, our construction achieves this by avoiding the Fujisaki-Okamoto transform and its impact on implementation security. Moreover, contrary to prior lattice-based identification protocols or standard constructions using signatures, our work does not require rejection sampling and can use more efficient parameters than signature schemes. We provide a generic construction from CPA-secured public key encryption schemes to identification protocols and give a security proof of the protocol in the ROM. Moreover, we instantiate the generic construction with Kyber, for which we use the proposed parameter sets for NIST security levels I, III, and V. To show that the protocol is suitable for constrained devices, we implemented one selected parameter set on an ARM Cortex-M4 microcontroller. As the protocol is based on existing algorithms for Kyber, we make use of existing SW components (e.g., fast NTT implementations) for our implementation.

We introduce Bicorn, an optimistically efficient distributed randomness protocol with strong robustness under a dishonest majority. Bicorn is a "commit-reveal-recover" protocol. Each participant commits to a random value, which are combined to produce a random output. If any participants fail to open their commitment, recovery is possible via a single time-lock puzzle which can be solved by any party. In the optimistic case, Bicorn is a simple and efficient two-round protocol with no time-lock puzzle. In either case, Bicorn supports open, flexible participation, requires only a public bulletin board and no group-specific setup or PKI, and is guaranteed to produce random output assuming any single participant is honest. All communication and computation costs are (at most) linear in the number of participants with low concrete overhead.

OPAQUE is an Asymmetric Password-Authenticated Key Exchange (aPAKE) protocol being standardized by the IETF (Internet Engineering Task Force) as a more secure alternative to the traditional ``password-over-TLS'' mechanism prevalent in current practice. OPAQUE defends against a variety of vulnerabilities of password-over-TLS by dispensing with reliance on PKI and TLS security, and ensuring that the password is never visible to servers or anyone other than the client machine where the password is entered. In order to facilitate the use of OPAQUE in practice, integration of OPAQUE with TLS is needed. The main proposal for standardizing such integration uses the Exported Authenticators (TLS-EA) mechanism of TLS 1.3 that supports post-handshake authentication and allows for a smooth composition with OPAQUE. We refer to this composition as TLS-OPAQUE and present a detailed security analysis for it in the Universal Composability (UC) framework.

Our treatment is general and includes the formalization of components that are needed in the analysis of TLS-OPAQUE but are of wider applicability as they are used in many protocols in practice. Specifically, we provide formalizations in the UC model of the notions of post-handshake authentication and channel binding. The latter, in particular, has been hard to implement securely in practice, resulting in multiple protocol failures, including major attacks against prior versions of TLS. Ours is the first treatment of these notions in a computational model with composability guarantees.

We complement the theoretical work with a detailed discussion of practical considerations for the use and deployment of TLS-OPAQUE in real-world settings and applications.

In the isogeny-based track of post-quantum cryptography the signature scheme SQISign relies on primes $p$ such that $p\pm1$ is smooth. In 2021 a new approach to find those numbers was discovered using solutions to the Prouhet-Tarry-Escott (PTE) problem. With these solutions one can sieve for smooth integers $A$ and $B$ with a difference of $|A-B|=C$ fixed by the solution. Then some $2A/C$ and $2B/C$ are smooth integers hopefully enclosing a prime. They took many different PTE solutions and combined them into a tree to process them more efficiently. But for bigger numbers there are fewer promising PTE solutions so their advantage over the naive approach (checking a single solution at a time) fades. For a single PTE solution the search can be optimised for the corresponding $C$ and allows to only sieve those integers that are divisible by $C$. In this work we investigate such optimisations and show a significant speed-up compared to the naive approach.

We study the post-quantum security of authenticated encryption (AE)schemes, designed with classical security in the mind. Under superposition attacks, many CBC-MAC variants have been broken, and AE modes employing those variants, such as EAX and GCM, thus fail at authenticity. As we show, the same modes are IND-qCPA insecure, i.e., fail to provide privacy under superposition attacks. However, a constrained version of GCM is IND-qCPA secure, and a nonce-based variant of the CBC-MAC is secure under superposition queries. Further, the combination of classical authenticity and classical chosen-plaintext privacy thwarts attacks with superposition chosen-ciphertext and classical chosen-plaintext queries -a security notion that we refer to as IND-qdCCA. And nonce-based key derivation allows to generically turn an IND-qdCCA secure scheme into an IND-qCCA secure scheme.

The sponge construction is a popular method for hashing. Quickly after its introduction, the sponge was proven to be tightly indifferentiable from a random oracle up to $ \approx 2^{c/2}$ queries, where $c$ is the capacity. However, this bound is not tight when the number of message blocks absorbed is restricted to $\ell <\lceil \frac{c}{2(b-c)}\rceil + 1$ (but still an arbitrary number of blocks can be squeezed). In this work, we show that this restriction leads to indifferentiability from a random oracle up to $\approx \min \left\{2^{b/2}, \max\left\{2^{c/2}, 2^{b- \ell \times (b-c)} \right\}\right\}$ queries, where $b>c$ is the permutation size. Depending on the parameters chosen, this result allows to have enhanced security or to absorb at a larger rate for applications that require a fixed-length input hash function.

Schnorr signatures are a popular choice due to their simplicity, provable security, and linear structure that enables relatively easy threshold signing protocols. The deterministic variant of Schnorr (where the nonce is derived in a stateless manner using a PRF from the message and a long term secret) is widely used in practice since it mitigates the threats of a faulty or poor randomness generator (which in Schnorr leads to catastrophic breaches of security). Unfortunately, threshold protocols for the deterministic variant of Schnorr have so far been quite inefficient, as they make non black-box use of the PRF involved in the nonce generation.

In this paper, we present the first two-party threshold protocol for Schnorr signatures, where signing is stateless and deterministic, and only makes black-box use of the underlying cryptographic algorithms.

We present a protocol from general assumptions which achieves covert security, and a protocol that achieves full active security under standard factoring-like assumptions. Our protocols make crucial use of recent advances within the field of pseudorandom correlation functions (PCFs). As an additional benefit, only two-rounds are needed to perform distributed signing in our protocol, connecting our work to a recent line of research on the trade-offs between round complexity and cryptographic assumptions for threshold Schnorr signatures.