International Association
for Cryptologic Research

The sponge is a popular construction for hashing and keyed hashing, and the duplex for authenticated encryption. They are proven to achieve approximately 2c/2 security, where c is the so-called capacity. This approach generalizes to arithmetizationoriented constructions, that operate on elements from a finite field of size p: in this case, security is guaranteed up to pc/2. However, to hash securely, the sponge needs to injectively pad the message, and likewise, authenticated encryption schemes often flip bits in the inner part to ensure domain separation. While these bit manipulations have little (but non-zero) influence on the efficiency and security in case of a field of size 2, they become more profound for larger fields. For example, Reinforced Concrete operates on a field with p ≈ 2256, absorbs 2 elements per permutation evaluation, and has a capacity c = 1. Consequently, injective padding results in superfluous permutation evaluations half of the time, and domain separation in the inner part would reduce the capacity to 0 and thus void security. In this work, we investigate an alternative approach to padding and domain separation for the sponge through the use of non-cryptographic permutations (NCPs) to transform the inner state. The idea dates back to the Merkle-Damgård with permutation construction (ASIACRYPT 2007) but we use it in a much more generalized form in the sponge and in the duplex. We demonstrate that this approach allows for NCP-based padding and NCP-based domain separation at a constant loss, regardless of the size of the field. We apply our findings to arithmetization-oriented element-wise sponging (akin to the recently introduced SAFE) and authenticated encryption.

The Ascon authenticated encryption scheme and hash function of Dobraunig et al. (Journal of Cryptology 2021) were recently selected as winner of the NIST lightweight cryptography competition. The mode underlying Ascon authenticated encryption (Ascon-AE) resembles ideas of SpongeWrap, but not quite, and various works have investigated the generic security of Ascon-AE, all covering different attack scenarios and with different bounds. This work systematizes knowledge on the mode security of Ascon-AE, and fills gaps where needed. We consider six mainstream security models, all in the multi-user setting: (i) nonce-respecting security, reflecting on the existing bounds of Chakraborty et al. (ASIACRYPT 2023, ACISP 2024) and Lefevre and Mennink (SAC 2024), (ii) nonce-misuse resistance, observing a non-fixable flaw in the proof of Chakraborty et al. (ACISP 2024), (iii) nonce-misuse resilience, delivering missing security analysis, (iv) leakage resilience, delivering a new security analysis that supersedes the informal proof sketch (though in a different model) of Guo et al. (ToSC 2020), (v) state-recovery security, expanding on the analysis of Lefevre and Mennink, and (vi) release of unverified plaintext, also delivering missing security analysis. We also match all bounds with tight attacks (up to constant and up to reasonable assumptions). As a bonus, we systematize the knowledge on Ascon-Hash and Ascon-PRF.

It is known that the sponge construction is tightly indifferentiable from a random oracle up to around 2c/2 queries, where c is the capacity. In particular, it cannot provide generic security better than half of the underlying permutation size. In this paper, we aim to achieve hash function security beating this barrier. We present a hashing mode based on two b-bit permutations named the double sponge. The double sponge can be seen as the sponge embedded within the double block length hashing paradigm, making two permutation calls in parallel interleaved with an efficient mixing function. Similarly to the sponge, the permutation size is split as b = r+c, and the underlying compression function absorbs r bits at a time. We prove that the double sponge is indifferentiable from a random oracle up to around 22c/3 queries. This means that the double sponge achieves security beyond the birthday bound in the capacity. In addition, if c > 3b/4, the double sponge beats the birthday bound in the primitive size, to our knowledge being the first hashing mode based on a permutation that accomplices this feature.

Hash chain based password systems are a useful way to guarantee authentication with one-time passwords. The core idea dates back to Lamport, and is specified in RFC 1760 as S/Key. At CCS 2017, Kogan et al. introduced T/Key, an improved password system where one-time passwords are only valid for a limited time period. They proved security of their construction in the random oracle model under a basic modeling of the adversary. In this work, we make various advances in the analysis and instantiation of hash chain based password systems. Firstly, we describe a slight abstraction called U/Key that allows for more flexibility in the instantiation and analysis, and we develop a security model that refines the adversarial strength into offline and online complexity, that can be used beyond the random oracle model, and that allows to argue multi-user security directly. Secondly, we derive a new security proof of U/Key in the random oracle model, as well as dedicated and tighter security proofs of U/Key instantiated with a sponge construction and a truncated permutation. These dedicated security proofs, in turn, solve a problem of understanding the preimage resistance of a cascaded evaluation of the sponge construction. When applied to T/Key, these results improve significantly over the earlier results: whereas the originally suggested instantiation using SHA-256 uses a compression function that maps 768 bits into 256 bits, with a truncated permutation construction one can generically achieve 128 bits of security already with a permutation of size 256 bits.

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 ≈ 2c/2 queries, where c is the capacity. However, this bound is not tight when the number of message blocks absorbed is restricted to ℓ < ⌈ c / 2(b−c) ⌉ + 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 ≈ min { 2b/2, max { 2c/2, 2b−ℓ×(b−c) }} 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.

We propose new algorithms for solving a class of large-weight syndrome decoding problems in random ternary codes. This is the main generic problem underlying the security of the recent Wave signature scheme (Debris-Alazard et al., 2019), and it has so far received limited attention. At SAC 2019 Bricout et al. proposed a reduction to a binary subset sum problem requiring many solutions, and used it to obtain the fastest known algorithm. However —as is often the case in the coding theory literature— its memory cost is proportional to its time cost, which makes it unattractive in most applications. In this work we propose a range of memory-efficient algorithms for this problem, which describe a near-continuous time-memory tradeoff curve. Those are obtained by using the same reduction as Bricout et al. and carefully instantiating the derived subset sum problem with exhaustive- search algorithms from the literature, in particular dissection (Dinur et al., 2012) and dissection in tree (Dinur, 2019). We also spend significant effort adapting those algorithms to decrease their granularity, thereby allowing them to be smoothly used in a syndrome decoding context when not all the solutions to the subset sum problem are required. For a proposed parameter set for Wave, one of our best instantiations is estimated to cost 2^177 bit operations and requiring 2^88.5 bits of storage, while we estimate this to be 2^152 and 2^144 for the best algorithm from Bricout et al..

The cryptographic sponge is a popular method for hash function design. The construction is in the ideal permutation model proven to be indifferentiable from a random oracle up to the birthday bound in the capacity of the sponge. This result in particular implies that, as long as the attack complexity does not exceed this bound, the sponge construction achieves a comparable level of collision, preimage, and second preimage resistance as a random oracle. We investigate these state-of-the-art bounds in detail, and observe that while the collision and second preimage security bounds are tight, the preimage bounds not tight. We derive an improved and tight preimage security bound for the cryptographic sponge construction. The result has direct implications for various lightweight cryptographic hash functions. For example, the NIST Lightweight Cryptography finalist Ascon-Hash does not generically achieve $2^{128}$ preimage security as claimed, but even $2^{192}$ preimage security. Comparable improvements are obtained for the modes of Spongent, PHOTON, ACE, Subterranean 2.0, and QUARK, among others.