The sponge is a popular construction of hash function design. It operates with a b-bit permutation on a b-bit state, that is split into a c-bit inner part and an r-bit outer part. However, the security bounds of the sponge are most often dominated by the capacity c: if the length of the digest is n bits, the construction tightly achieves min{n/2,c/2} -bit collision resistance, min{n,c/2} -bit second preimage resistance, and min{n,max{n-r,c/2}} -bit preimage resistance. Here, it is noteworthy that the generic attacks matching the preimage and second preimage bounds make use of the inverse of the permutation. We demonstrate that, by a relatively simple adjustment, significantly improved preimage and second preimage resistance can be achieved. In detail, we first present the - construction, that differs from the sponge by evaluating the permutation during absorption in a Davies-Meyer mode. This construction generically achieves min{n/2,c/2} -bit collision resistance as the sponge does, but n-bit preimage resistance and min{n,c-log _2(α )} -bit second preimage resistance, where α is the maximum size of the first preimage in blocks. Next, we investigate how improved security can be achieved with a smaller feed-forward, and we present the -^a family of functions, indexed by a parameter a∈{0,… ,b} . These functions replace the permutation during absorption in the sponge by an Encrypted Davies-Meyer mode, but with only a bits of feed-forward. For a=b , comparable bounds as for - are obtained, and these bounds gradually decrease to the original sponge bounds for decreasing values of a. We present various instantiations of - and -^a using the Keccak and Ascon permutations, and concretely demonstrate the immediate security and performance gains of these instances. For example, one can achieve up to 512-bit preimage and second preimage resistance using the 800-bit Keccak permutation (rather than 1600-bit in SHA-3), and likewise, one can use the 1600-bit Keccak permutation to easily achieve up to 1024-bit preimage and second preimage resistance (therewith properly fitting within the recently announced Chinese call for a new generation of cryptographic algorithms). Finally, we show the benefits of using these instantiations in the context of hash-based signature schemes whose security relies solely on the (second) preimage resistance of the underlying hash functions (such as - ).

A vast body of work studies how to build a pseudorandom function (PRF) from a pseudorandom permutation (PRP) with beyond-the-birthday-bound (BBB) security. Often, such constructions are also expected to offer some security in keyless settings, for example in the context of committing security or to substitute a parallelizable short-input random oracle (RO) if used in counter mode. This has spurred several works on keyless variants of PRP-to-PRF constructions. However, recent works (Gunsing et al., CRYPTO 2022, 2023) reveal flaws in almost all existing proofs, painting a grim picture. This paper clarifies the situation with an in-depth analysis of RP-based short-input RF constructions. First, we categorize all two-call short-input/output RP-to-RF constructions and evaluate their indifferentiability level. We introduce the “chaining attack”, a powerful, widely applicable differentiability attack. When applied to the sum of a permutation and its inverse, it invalidates an earlier result (Dodis et al., EUROCRYPT 2008). On the positive side, we show that only the Sum Of Permutations and Encrypted Davies-Meyer Dual, when instantiated with independent permutations, achieve BBB security and could potentially yield a parallelizable short-input RO. Second, we study the indifferentiability of expanding RP-to-RF constructions and show that _w , the core PRF underlying CENC, achieves BBB security. As side effects, we obtain a simplified proof of indifferentiability for Sum of Permutations, and the committing security of CENC.

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.

Masking is a commonly used countermeasure against side-channel attacks, encoding secrets into multiple shares such that each share leaks only partial information. A longstanding question is under what noise conditions masking guarantees security, and how this security scales with the number of shares. While sufficient conditions have been known for binary fields and in high-noise regimes, the borderline and low-noise cases have remained poorly understood. In this work, we close this gap through a decomposition-based analysis. Our approach reduces leakage in extended fields to binary projections, enabling tight bounds on the adversary’s success rate and yielding an optimal reduction from the noisy leakage model to the random probing model—even in regimes where classical reductions fail. As a central theoretical result, we prove a conjecture of Dziembowski et al. (TCC 2016), showing that for any additive group 𝔾 with largest proper subgroup ℍ , masking strictly improves security whenever the leakage is δ -noisy with δ < 1 - |ℍ||𝔾| . We additionally demonstrate the practical relevance of our framework for leakage certification and for determining the required masking order under realistic low-noise conditions. Our results unify and sharpen the understanding of noise requirements for masking, advancing both the theoretical foundations and the practical evaluation of side-channel countermeasures.

The Ascon authenticated encryption scheme has recently been selected as winner of the NIST Lightweight Cryptography competition. Despite its fame, a comprehensive and self-contained generic security treatment of its mode remains absent. In this work we present a thorough security analysis of the Ascon mode: we consider multi-user and possibly nonce-misuse security by default, but more importantly, we particularly investigate the role of the key blinding. More technically, our analysis includes an authenticity study in various attack settings. This analysis includes a description of a security model of authenticity under state recovery, that captures the idea that the mode aims to still guarantee authenticity and security against key recovery even if an inner state is revealed to the adversary in some way, for instance through leakage. We prove that Ascon satisfies this security property, thanks to its unique key blinding technique.

A classical way to turn a cryptographic hash function into a MAC (message authentication code) function is by concatenating key and message and interpreting the result as a tag. For the Merkle-Damgård hash function construction, the approach to prepend the key to the message is known to be insecure, as it is vulnerable to the length extension attack. This observation eventually resulted in the introduction of the HMAC construction. The alternative approach to append the key to the message, even though it already dates back to a work of Tsudik from 1992, has never been investigated in detail. In this work, we perform an in-depth treatment on the possibilities to design a MAC function from the Merkle-Damgård hash function construction by processing the key at the suffix. We formalize two constructions: the suffix keyed Merkle-Damgård construction that simply appends key to message, and the suffix blinded Merkle-Damgård construction that blinds the state before compressing the last message, much like the suffix keyed sponge construction (SuKS). We subsequently prove that both constructions are secure in the standard model under reasonable assumptions on the underlying compression function. We finally investigate the security of these constructions in the leaky setting, and demonstrate that the suffix keyed Merkle-Damgård construction is not leakage resilient, but the suffix blinded Merkle-Damgård construction is leakage resilient as long as an appropriate padding rule is adopted and as long as the underlying building blocks are processing secret data in a leakage resilient manner.

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.

The sum of permutations is a popular way to turn a PRP (like a block cipher) into a PRF. However, with the rise of permutation based cryptography, it makes sense to investigate the possibility to design a PRF as the sum of externally keyed public permutations. This challenge was initiated by Chen et al. (CRYPTO 2019) who presented the Sum of Even-Mansours (SoEM) construction. Sibleyras and Todo (CT-RSA 2023) later minimized the amount of key maskings in this construction with their Keyed Sum of Permutations (KSoP). However, both constructions have in common that their security proofs require two independent keys and two independent public random permutations. In this work, we investigate the possibilities to reduce this amount of randomness, by introducing three constructions: sirP, that uses two independent permutations but one key, sirK, that uses two independent keys but one permutation, and sirX, that uses a single permutation and a single key. The constructions are further generalized by having a parameter prescribing the data input size compared to the permutation size. We present general security results for all three variants, and demonstrate that, for certain parameter choices, the security bounds match those of SoEM and KSoP, but with reduced randomness.

Side-channel attacks (SCAs) pose a significant threat to the implementations of lightweight ciphers, particularly in resource-constrained environments where masking—the primary countermeasure—is constrained by tight resource limitations. This makes it crucial to reduce the resource and randomness requirements of masking schemes. In this work, we investigate an approach to minimize the randomness complexity of masking algorithms. Specifically, we explore the theoretical foundations of higher-order masking schemes that eliminate the need for online (fresh) randomness by relying solely on offline randomness present in the initial input shares. We demonstrate that round-based ciphers with linear diffusion layers can support such deterministic composition, where the diffusion layer acts as a refresh subcircuit. This ensures that, up to a threshold number, probes placed across rounds remain independent. Based on this observation, we propose composition theorems for probing-secure masking. On the practical side, we instantiate our framework using known deterministic first- and second-order masked S-boxes and provide software implementations of Ascon’s protected permutation.

A tweakable wide blockcipher is a construction which behaves in the same way as a tweakable blockcipher, with the difference that the actual block size is flexible. Due to this feature, a tweakable wide blockcipher can be directly used as a strong encryption scheme that provides full diffusion when encrypting plaintexts to ciphertexts and vice versa. Furthermore, it can be the basis of authenticated encryption schemes fulfilling the strongest security notions. In this paper, we present three instantiations of the docked double decker tweakable wide blockcipher: ddd - AES , ddd - AES ^+ , and bbb - ddd - AES . These instances exclusively use similar building blocks as AES-GCM (AES and finite field multiplication), are designed for maximal parallelism, and hence, can make efficient use of existing hardware accelerators. ddd - AES is a birthday bound secure scheme, and ddd - AES ^+ is an immediate generalization to allow for variable length tweaks. bbb - ddd - AES achieves security beyond the birthday bound provided that the same tweak is not used too often. Moreover, bbb - ddd - AES builds upon a novel conditionally beyond birthday bound secure pseudorandom function, a tweakable variant of the XOR of permutations, facilitating in the need to include a tweak in the AES evaluations without sacrificing flexibility in docked double decker. We furthermore introduce an authenticated encryption mode aaa specifically tailored to be instantiated with ddd - AES and bbb - ddd - AES , where special attention is given to how the nonce and associated data can be processed. We prove that this mode is secure in the nonce-respecting setting, in the nonce-misuse setting, as well as in the setting where random nonces are used. We finally present a comparison with other tweakable wide blockciphers, give a high-level idea of the efficiency potential of our schemes, and provide benchmarks that confirm this idea.

The development of the Linux kernel has been a long ongoing project. Recent modernization efforts have prompted its developers to revisit legacy code, including the 'random.c' driver. This critical component is most notably responsible for supplying the system with random values. However, recent changes to this driver rely on untested assumptions, with limited support in the literature. In this work, we perform an in-depth study of the entropy accumulation process. We first analyze the density distribution of its entropic inputs. Then, we use this knowledge to run a simulation in which various accumulation functions, ranging from the simpler rotation function to the SipHash-based function used in the latest driver, are compared using statistical tests. Finally, we verify these results computationally. Our findings show that the inputs to Linux's Random Number Generator are neither independent nor identically distributed, as was previously assumed. We show instead that the various inputs are all dependent on previous values, and each follow a different distribution. Our results also confirm that the SipHash-based function introduced in version 5.18 is indeed an improvement over its predecessors, as it condenses more entropy than the alternatives for the given range of inputs.

Authenticated encryption schemes guarantee that parties who share a secret key can communicate confidentially and authentically. One of the most popular and widely used authenticated encryption schemes is GCM by McGrew and Viega (INDOCRYPT 2004). However, despite its simplicity and efficiency, GCM also comes with its deficiencies, most notably devastating insecurity against nonce-misuse and imperfect security for short tags. Very recently, Campagna, Maximov, and Mattsson presented GCM-SST (IETF Internet draft 2024), a variant of GCM that uses a slightly more involved universal hash function composition, and claimed that this construction achieves stronger security in case of tag truncation. GCM-SST already received various interest from industries (e.g., Amazon and Ericsson) and international organizations (e.g., IETF and 3GPP) but it has not received any generic security analysis to date. In this work, we fill this gap and perform a detailed security analysis of GCM-SST. In particular, we prove that GCM-SST achieves security in the nonce-misuse resilience model of Ashur et al. (CRYPTO 2017), roughly guaranteeing that even if nonces are reused, evaluations of GCM-SST for new nonces are secure. Our security bound also verified the designers' (informal) claim on tag truncation. Additionally, we investigate and describe possibilities to optimize the hashing in GCM-SST further, and we describe a universal forgery attack in a complexity of around 2(33.6), improving over an earlier attack of 240 complexity of Lindell, when the tag is 32 bits.

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.

In this work we present the COLM authenticated encryption (AE) scheme which is the second of the two winners in the defense in depth category of the CAESAR competition. COLM realizes a nonce-based authenticated encryption with associated data and uses the popular AES blockcipher as its underlying primitive. We propose two possible blockcipher instantiations (with key of length 128 or 256 bits). We also define two COLM modes of operation variants: a primary COLM _0 mode for general purpose applications, and a COLM _τ variant with intermediate tag generation/verification geared to support low-end devices and applications where frequent verification is required. COLM is designed with security, simplicity, and efficiency in mind. The main design goal of COLM is high security: a primary feature of the defense in depth CAESAR category. COLM provides security beyond the traditional AE security. First, COLM is secure against nonce misuse, namely, it enables security in adversarial settings where the nonce inputs to the AE scheme repeat. In contrast to standardized and popular AE algorithms, such as GCM and OCB1-3 modes, whose AE security trivially breaks down when the nonce is repeated, COLM ensures both confidentiality and authenticity (AE) security with repeated nonces. Second, our COLM _τ variant enables increased security levels in situations where release of unverified ciphertext (RUP) occurs due to its ability to limit a potential leakage by frequent verifications. In this work we prove COLM secure with respect to both confidentiality and authenticity (AE) security under nonce misuse in the well-known provable security framework. Our proofs show that COLM maintains n/2-bit security levels for block sizes of n bits. Furthermore, due to the inherent parallelism on both mode and primitive levels, our software performance results show that the price paid for enhanced security does come at the cost of minimal efficiency losses. More concretely, we implement GCM, COLM, and Deoxys-II on the Kaby Lake and Coffee lake Intel platforms. Compared to the other winner in the defense in depth category Deoxys-II, our AE design COLM _0 performs 10–20 _0 is around 5

Lightweight cryptographic constructions are often optimized on multiple aspects that put the security bounds to the limit. In this respect, it is important to obtain security bounds that are tight and give an accurate and exact indication of the generic security. However, whereas for black-box security bounds it has become common practice to argue tightness of security bounds, for leakage resilience security bounds this is not the case. This is unfortunate, as for leakage resilience results, tightness is even more important as there is already a lossiness incurred in capturing the actual leakage by a theoretical model in the first place. In this work, we consider the SuKS (Suffix Keyed Sponge) PRF construction and investigate tightness of the leakage resilience bound of Dobraunig and Mennink (ToSC 2019). We observe that, although their black-box security result is tight, their leakage resilience bound is not tight in their bounded leakage term λ. We observe that this is caused by the fact that parts of the security bound contain a term covering multicollisions and a term covering leakage, but an adversary is unable to combine both. We next consider improved security of the SuKS for two types of leakage: fixed position leakage, where the adversary directly learns the value of λ bits of a secret state, and Hamming weight leakage, where the Hamming weight of a fixed part of the state is leaked. For fixed position leakage, a very generous form of bounded leakage, we improve the original bound by making wise use of the multicollision limit function of Daemen et al. (ASIACRYPT 2017). For the more realistic setting of Hamming weight leakage, we structurally revisit the multicollision limit function analysis by including Hamming weight in the computation, a problem that is difficult on its own due to the non-uniform character of this type of leakage. In both cases, we improve and tighten the leakage resilience bound of Dobraunig and Mennink. The improved bound for the SuKS has immediate consequences for the leakage resilience of the NIST lightweight cryptography competition finalist ISAP v2, an authenticated encryption scheme that uses the SuKS internally.

The duplex construction is already well analyzed with many papers proving its security in the random permutation model. However, so far, the first phase of the duplex, where the state is initialized with a secret key and an initialization vector ( $$ IV $$ ), is typically analyzed in a worst case manner. More detailed, it is always assumed that the adversary is allowed to choose the $$ IV $$ at will. However, in practice, the adversary can be stripped of its power to control the $$ IV $$ in several ways. One prominent way of doing this is the use of a nonce ( $$ IV $$ ) masked with a secret, as done in AES-GCM in TLS 1.3. In this paper, we analyze how the security of the duplex construction changes if restrictions on the choice of the $$ IV $$ are imposed. In particular, we evaluate several strategies that can achieve this, varying from the $$ IV $$ on key case over the global nonce case to the random $$ IV $$ case. We apply our findings to duplex-based encryption and authenticated encryption, compare the different strategies, and discuss the practical applications of our results.