International Association
for Cryptologic Research

Virtually all modern blockciphers are {\it 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 {\it 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 {\it 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 blockciphers 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.

At EUROCRYPT 2015, Cogliati and Seurin proved that the 4-round Iterated Even-Mansour (IEM) cipher with Independent random Permutations and no key schedule EMIP4(k, u) = k⊕p4 ( k⊕p3 ( k⊕p2 (k⊕p1 (k⊕u)))) is sequentially indifferentiable from an ideal cipher, which implies chosen-key security in the sense of correlation intractability. In practice, however, blockciphers such as the AES typically employ the same permutation at each round. To bridge the gap, we prove that the 4-round IEM cipher EMSP[φ]p4 (k, u) = k4⊕p (k3⊕p (k2⊕p(k1⊕p(k0⊕u)))), whose round keys ki = φi(k) are derived using an affine permutation φ : {0, 1}n → {0, 1}n with certain properties, is sequentially indifferentiable from an ideal cipher. The function φ can be a linear orthomorphism, or φ(k) := k≫a for some fixed integer a using cyclic shift. To our knowledge, this is the first indifferentiability-type result for blockciphers using identical round functions.

Security against side-channels and faults is a must for the deployment of embedded cryptography. A wide body of research has investigated solutions to secure implementations against these attacks at different abstraction levels. Yet, to a large extent, current solutions focus on one or the other threat. In this paper, we initiate a mode-level study of cryptographic primitives that can ensure security in a (new and practically-motivated) adversarial model combining leakage and faults. Our goal is to identify constructions that do not require a uniform protection of all their operations against both attack vectors. For this purpose, we first introduce a versatile and intuitive model to capture leakage and faults. We then show that a MAC from Asiacrypt 2021 natively enables a leveled implementation for fault resilience where only its underlying tweakable block cipher must be protected, if only the tag verification can be faulted. We finally describe two approaches to amplify security for fault resilience when also the tag generation can be faulted. One is based on iteration and requires the adversary to inject increasingly large faults to succeed. The other is based on randomness and allows provable security against differential faults.

Symmetric-key primitives designed over the prime field Fp with odd characteristics, rather than the traditional Fn2 , are becoming the most popular choice for MPC/FHE/ZK-protocols for better efficiencies. However, the security of Fp is less understood as there are highly nontrivial gaps when extending the cryptanalysis tools and experiences built on Fn2 in the past few decades to Fp.At CRYPTO 2015, Sun et al. established the links among impossible differential, zero-correlation linear, and integral cryptanalysis over Fn2 from the perspective of distinguishers. In this paper, following the definition of linear correlations over Fp by Baignères, Stern and Vaudenay at SAC 2007, we successfully establish comprehensive links over Fp, by reproducing the proofs and offering alternatives when necessary. Interesting and important differences between Fp and Fn2 are observed.- Zero-correlation linear hulls can not lead to integral distinguishers for some cases over Fp, while this is always possible over Fn2proven by Sun et al..- When the newly established links are applied to GMiMC, its impossible differential, zero-correlation linear hull and integral distinguishers can be increased by up to 3 rounds for most of the cases, and even to an arbitrary number of rounds for some special and limited cases, which only appeared in Fp. It should be noted that all these distinguishers do not invalidate GMiMC’s security claims.The development of the theories over Fp behind these links, and properties identified (be it similar or different) will bring clearer and easier understanding of security of primitives in this emerging Fp field, which we believe will provide useful guides for future cryptanalysis and design.

Picnic is a NIST PQC Round 3 Alternate signature candidate that builds upon symmetric primitives following the MPC-in-the-head paradigm. Recently, researchers have been exploring more secure/efficient signature schemes from conservative one-way functions based on AES, or new low complexity one-way functions like Rain (CCS 2022) and AIM (CCS 2023). The signature schemes based on Rain and AIM are currently the most efficient among MPC-in-the-head-based schemes, making them promising post-quantum digital signature candidates. However, the exact hardness of these new one-way functions deserves further study and scrutiny. This work presents algebraic attacks on Rain and AIM for certain instances, where one-round Rain can be compromised in $2^{n/2}$ for security parameter $n\in \{128,192,256\}$, and two-round Rain can be broken in $2^{120.3}$, $2^{180.4}$, and $2^{243.1}$ encryptions, respectively. Additionally, we demonstrate an attack on AIM-III (which aims at 192-bit security) with a complexity of $2^{186.5}$ encryptions. These attacks exploit the algebraic structure of the power function over fields with characteristic 2, which provides potential insights into the algebraic structures of some symmetric primitives and thus might be of independent interest.

To counter side-channel attacks, a masking scheme randomly encodes keydependent variables into several shares, and transforms operations into the masked correspondence (called gadget) operating on shares. This provably achieves the de facto standard notion of probing security.We continue the long line of works seeking to reduce the overhead of masking. Our main contribution is a new masking scheme over finite fields in which shares of different variables have a part in common. This enables the reuse of randomness / variables across different gadgets, and reduces the total cost of masked implementation. For security order d and circuit size l, the randomness requirement and computational complexity of our scheme are Õ(d2) and Õ(ld2) respectively, strictly improving upon the state-of-the-art Õ(d2) and Õ(ld3) of Coron et al. at Eurocrypt 2020.A notable feature of our scheme is that it enables a new paradigm in which many intermediates can be precomputed before executing the masked function. The precomputation consumes Õ(ld2) and produces Õ(ld) variables to be stored in RAM. The cost of subsequent (online) computation is reduced to Õ(ld), effectively speeding up e.g., challenge-response authentication protocols. We showcase our method on the AES on ARM Cortex M architecture and perform a T-test evaluation. Our results show a speed-up during the online phase compared with state-of-the-art implementations, at the cost of acceptable RAM consumption and precomputation time.To prove security for our scheme, we propose a new security notion intrinsically supporting randomness / variables reusing across gadgets, and bridging the security of parallel compositions of gadgets to general compositions, which may be of independent interest.

Motivated by the recent trend towards low multiplicative complexity blockciphers (e.g., Zorro, CHES 2013; LowMC, EUROCRYPT 2015; HADES, EUROCRYPT 2020; MALICIOUS, CRYPTO 2020), we study their underlying structure partial SPNs, i.e., Substitution-Permutation Networks (SPNs) with parts of the substitution layer replaced by an identity mapping, and put forward the first provable security analysis for such partial SPNs built upon dedicated linear layers. For different instances of partial SPNs using MDS linear layers, we establish strong pseudorandom security as well as practical provable security against impossible differential attacks. By extending the well-established MDS code-based idea, we also propose the first principled design of linear layers that ensures optimal differential propagation. Our results formally confirm the conjecture that partial SPNs achieve the same security as normal SPNs while consuming less non-linearity, in a well-established framework.

The security proofs of leakage-resilient MACs based on symmetric building blocks currently rely on idealized assumptions that hardly translate into interpretable guidelines for the cryptographic engineers implementing these schemes. In this paper, we first present a leakage-resilient MAC that is both efficient and secure under standard and easily interpretable black box and physical assumptions. It only requires a collision resistant hash function and a single call per message authentication to a Tweakable Block Cipher (TBC) that is unpredictable with leakage. This construction leverages two design twists: large tweaks for the TBC and a verification process that checks the inverse TBC against a constant. It enjoys beyond birthday security bounds. We then discuss the cost of getting rid of these design twists. We show that security can be proven without them as well. Yet, a construction without large tweaks requires stronger (non idealized) assumptions and inevitably incurs performance overheads if specialized TBCs can be exploited, and a construction without twisted verification requires even stronger assumptions (still non idealized) and leads to more involved bounds. The combination of these results makes a case for our first pragmatic construction and suggests the design of TBCs with large tweaks and good properties for side-channel countermeasures as an interesting challenge.

We revisit the security of various generalized Feistel networks. Concretely, for unbalanced, alternating, type-1, type-2, and type-3 Feistel networks built from random functions, we substantially improve the coupling analyzes of Hoang and Rogaway (CRYPTO 2010). For a tweakable blockcipher-based generalized Feistelnetwork proposed by Coron et al. (TCC 2010), we present a coupling analysis and for the first time show that with enough rounds, it achieves 2n-bit security, and this provides highly secure, double-length tweakable blockciphers.

We investigate constructing message authentication schemes from symmetric cryptographic primitives, with the goal of achieving security when most intermediate values during tag computation and verification are leaked (i.e., mode-level leakage-resilience). Existing efficient proposals typically follow the plain Hash-then-MAC paradigm T = TGenK(H(M)). When the domain of the MAC function TGenK is {0, 1}128, e.g., when instantiated with the AES, forgery is possible within time 264 and data complexity 1. To dismiss such cheap attacks, we propose two modes: LRW1-based Hash-then-MAC (LRWHM) that is built upon the LRW1 tweakable blockcipher of Liskov, Rivest, and Wagner, and Rekeying Hash-then-MAC (RHM) that employs internal rekeying. Built upon secure AES implementations, LRWHM is provably secure up to (beyond-birthday) 278.3 time complexity, while RHM is provably secure up to 2121 time. Thus in practice, their main security threat is expected to be side-channel key recovery attacks against the AES implementations. Finally, we benchmark the performance of instances of our modes based on the AES and SHA3 and confirm their efficiency.

In this paper, we propose Tweak-aNd-Tweak (TNT for short) mode, which builds a tweakable block cipher from three independent block ciphers. TNT handles the tweak input by simply XOR-ing the unmodified tweak into the internal state of block ciphers twice. Due to its simplicity, TNT can also be viewed as a way of turning a block cipher into a tweakable block cipher by dividing the block cipher into three chunks, and adding the tweak at the two cutting points only. TNT is proven to be of beyond-birthday-bound $2^{2n/3}$ security, under the assumption that the three chunks are independent secure $n$-bit SPRPs. It clearly brings minimum possible overhead to both software and hardware implementations. To demonstrate this, an instantiation named TNT-AES with 6, 6, 6 rounds of AES as the underlying block ciphers is proposed. Besides the inherent proven security bound and tweak-independent rekeying feature of the TNT mode, the performance of TNT-AES is comparable with all existing TBCs designed through modular methods.

The ongoing NIST lightweight cryptography standardization process highlights the importance of resistance to side-channel attacks, which has renewed the interest for Authenticated Encryption schemes (AEs) with light(er)-weight sidechannel secure implementations. To address this challenge, our first contribution is to investigate the leakage-resistance of a generic duplex-based stream cipher. When the capacity of the duplex is of c bits, we prove the classical bound, i.e., ≈ 2c/2, under an assumption of non-invertible leakage. Based on this, we propose a new 1-pass AE mode TETSponge, which carefully combines a tweakable block cipher that must have strong protections against side-channel attacks and is scarcely used, and a duplex-style permutation that only needs weak side-channel protections and is used to frugally process the message and associated data. It offers: (i) provable integrity (resp. confidentiality) guarantees in the presence of leakage during both encryption and decryption (resp. encryption only), (ii) some level of nonce misuse robustness. We conclude that TETSponge is an appealing option for the implementation of low-energy AE in settings where side-channel attacks are a concern. We also provides the first rigorous methodology for the leakage-resistance of sponge/duplex-based AEs based on a minimal non-invertibility assumption on leakages, which leads to various insights on designs and implementations.

We study the concrete security of high-performance implementations of half-gates garbling, which all rely on (hardware-accelerated) AES. We find that current instantiations using k-bit wire labels can be completely broken—in the sense that the circuit evaluator learns all the inputs of the circuit garbler—in time O(2k/C), where C is the total number of (non-free) gates that are garbled, possibly across multiple independent executions. The attack can be applied to existing circuit-garbling libraries using k = 80 when C ≈ $10^9$, and would require 267 machine-months and cost about $3500 to implement on the Google Cloud Platform. Since the attack can be entirely parallelized, the attack could be carried out in about a month using ≈ 250 machines. With this as our motivation, we seek a way to instantiate the hash function in the half-gates scheme so as to achieve better concrete security. We present a construction based on AES that achieves optimal security in the single-instance setting (when only a single circuit is garbled). We also show how to modify the half-gates scheme so that its concrete security does not degrade in the multi-instance setting. Our modified scheme is as efficient as prior work in networks with up to 2 Gbps bandwidth.

This paper defines Spook: a sponge-based authenticated encryption with associated data algorithm. It is primarily designed to provide security against side-channel attacks at a low energy cost. For this purpose, Spook is mixing a leakageresistant mode of operation with bitslice ciphers enabling efficient and low latency implementations. The leakage-resistant mode of operation leverages a re-keying function to prevent differential side-channel analysis, a duplex sponge construction to efficiently process the data, and a tag verification based on a Tweakable Block Cipher (TBC) providing strong data integrity guarantees in the presence of leakages. The underlying bitslice ciphers are optimized for the masking countermeasures against side-channel attacks. Spook is an efficient single-pass algorithm. It ensures state-of-the-art black box security with several prominent features: (i) nonce misuse-resilience, (ii) beyond-birthday security with respect to the TBC block size, and (iii) multiuser security at minimum cost with a public tweak. Besides the specifications and design rationale, we provide first software and hardware implementation results of (unprotected) Spook which confirm the limited overheads that the use of two primitives sharing internal components imply. We also show that the integrity of Spook with leakage, so far analyzed with unbounded leakages for the duplex sponge and a strongly protected TBC modeled as leak-free, can be proven with a much weaker unpredictability assumption for the TBC. We finally discuss external cryptanalysis results and tweaks to improve both the security margins and efficiency of Spook.

Triggered by the increasing deployment of embedded cryptographic devices (e.g., for the IoT), the design of authentication, encryption and authenticated encryption schemes enabling improved security against side-channel attacks has become an important research direction. Over the last decade, a number of modes of operation have been proposed and analyzed under different abstractions. In this paper, we investigate the practical consequences of these findings. For this purpose, we first translate the physical assumptions of leakage-resistance proofs into minimum security requirements for implementers. Thanks to this (heuristic) translation, we observe that (i) security against physical attacks can be viewed as a tradeoff between mode-level and implementation-level protection mechanisms, and (i}) security requirements to guarantee confidentiality and integrity in front of leakage can be concretely different for the different parts of an implementation. We illustrate the first point by analyzing several modes of operation with gradually increased leakage-resistance. We illustrate the second point by exhibiting leveled implementations, where different parts of the investigated schemes have different security requirements against leakage, leading to performance improvements when high physical security is needed. We finally initiate a comparative discussion of the different solutions to instantiate the components of a leakage-resistant authenticated encryption scheme.

Recent works of Cogliati et al. (CRYPTO 2018) have initiated provable treatments of Substitution-Permutation Networks (SPNs), one of the most popular approach to construct modern blockciphers. Such theoretical SPN models may employ non-linear diffusion layers, which enables beyond-birthday-bound provable security. Though, for the model of real world blockciphers, i.e., SPN models with linear diffusion layers, existing provable results are capped at birthday security up to $2^{n/2}$ adversarial queries, where $n$ is the size of the idealized S-boxes. In this paper, we overcome this birthday barrier and prove that a 4-round SPN with linear diffusion layers and independent round keys is secure up to $2^{2n/3}$ queries. For this, we identify conditions on the linear layers that are sufficient for such security, which, unsurprisingly, turns out to be slightly stronger than Cogliati et al.'s conditions for birthday security. These provides additional theoretic supports for real world SPN blockciphers.

Tweakable block ciphers (TBCs) have been established as a valuable replacement for many applications of classical block ciphers. While several dedicated TBCs have been proposed in the previous years, generic constructions that build a TBC from a classical block cipher are still highly useful, for example, to reuse an existing implementation. However, most generic constructions need an additional call to either the block cipher or a universal hash function to process the tweak, which limited their efficiency. To address this deficit, Bao et al. proposed Tweak-aNd-Tweak (TNT) at EUROCRYPT'20. Their construction chains three calls to independent keyed permutations and adds the unmodified tweak to the state in between the calls. They further suggested an efficient instantiation TNT-AES that was based on round-reduced AES for each of the permutations. Their work could prove 2n/3-bit security for their construction, where n is the block size in bits. Though, in the absence of an upper bound, their analysis had to consider all possible attack vectors with up to 2^n time, data, and memory. Still, closing the gap between both bounds remained a highly interesting research question. In this work, we show that a variant of Mennink's distinguisher on CLRW2 with O(sqrt{n} 2^{3n/4}) data and O(2^{3n/2}) time from TCC'18 also applies to TNT. We reduce its time complexity to O(sqrt{n} 2^{3n/4}), show the existence of a second similar distinguisher, and demonstrate how to transform the distinguisher to a key-recovery attack on TNT-AES[5,*,*] from an impossible differential. From a constructive point of view, we adapt the rigorous STPRP analysis of CLRW2 by Jha and Nandi to show O(2^{3n/4}) TPRP security for TNT. Thus, we move towards closing the gap between the previous proof and attacks for TNT as well as its proposed instance.

Higher-order masking countermeasures provide strong provable security against side-channel attacks at the cost of incurring significant overheads, which largely hinders its applicability. Previous works towards remedying cost mostly concentrated on ``local'' calculations, i.e., optimizing the cost of computation units such as a single AND gate or a field multiplication. This paper explores a complementary ``global'' approach, i.e., considering multiple operations in the masked domain as a batch and reducing randomness and computational cost via amortization. In particular, we focus on the amortization of $\ell$ parallel field multiplications for appropriate integer $\ell > 1$, and design a kit named {\it packed multiplication} for implementing such a batch. Higher-order masking countermeasures provide strong provable security against side-channel attacks at the cost of incurring significant overheads, which largely hinders its applicability. Previous works towards remedying cost mostly concentrated on ``local'' calculations, i.e., optimizing the cost of computation units such as a single AND gate or a field multiplication. This paper explores a complementary ``global'' approach, i.e., considering multiple operations in the masked domain as a batch and reducing randomness and computational cost via amortization. In particular, we focus on the amortization of $\ell$ parallel field multiplications for appropriate integer $\ell > 1$, and design a kit named {\it packed multiplication} for implementing such a batch. For $\ell+d\leq2^m$, when $\ell$ parallel multiplications over $\mathbb{F}_{2^{m}}$ with $d$-th order probing security are implemented, packed multiplication consumes $d^2+2\ell d + \ell$ bilinear multiplications and $2d^2 + d(d+1)/2$ random field variables, outperforming the state-of-the-art results with $O(\ell d^2)$ multiplications and $\ell \left \lfloor d^2/4\right \rfloor + \ell d$ randomness. To prove $d$-probing security for packed multiplications, we introduce some weaker security notions for multiple-inputs-multiple-outputs gadgets and use them as intermediate steps, which may be of independent interest. As parallel field multiplications exist almost everywhere in symmetric cryptography, lifting optimizations from ``local'' to ``global'' substantially enlarges the space of improvements. To demonstrate, we showcase the method on the AES Subbytes step, GCM and TET (a popular disk encryption). Notably, when $d=8$, our implementation of AES Subbytes in ARM Cortex M architecture achieves a gain of up to $33\%$ in total speeds and saves up to $68\%$ random bits than the state-of-the-art bitsliced implementation reported at ASIACRYPT~2018.

We propose TEDT, a new Authenticated Encryption with Associated Data (AEAD) mode leveraging Tweakable Block Ciphers (TBCs). TEDT provides the following features: (i) It offers full leakage-resistance, that is, it limits the exploitability of physical leakages via side-channel attacks, even if these leakages happen during every message encryption and decryption operation. Moreover, the leakage integrity bound is asymptotically optimal in the multi-user setting. (ii) It offers nonce misuse-resilience, that is, the repetition of nonces does not impact the security of ciphertexts produced with fresh nonces. (iii) It can be implemented with a remarkably low energy cost when strong resistance to side-channel attacks is needed, supports online encryption and handles static and incremental associated data efficiently. Concretely, TEDT encourages so-called leveled implementations, in which two TBCs are implemented: the first one needs strong and energy demanding protections against side-channel attacks but is used in a limited way, while the other only requires weak and energy-efficient protections and performs the bulk of the computation. As a result, TEDT leads to more energy-efficient implementations compared to traditional AEAD schemes, whose side-channel security requires to uniformly protect every (T)BC execution.

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.

Key-Alternating Feistel (KAF) ciphers, a.k.a. Feistel-2 models, refer to Feistel networks with round functions of the form $$F_i(k_i\oplus x_i)$$, where $$k_i$$ is the (secret) round-key and $$F_i$$ is a public random function. This model roughly captures the structures of many famous Feistel ciphers, and the most prominent instance is DES.Existing provable security results on KAF assumed independent round-keys and round functions (ASIACRYPT 2004 & FSE 2014). In this paper, we investigate how to achieve security under simpler and more realistic assumptions: with round-keys derived from a short main-key, and hopefully with identical round functions.For birthday-type security, we consider 4-round KAF, investigate the minimal conditions on the way to derive the four round-keys, and prove that when such adequately derived keys and the same round function are used, the 4-round KAF is secure up to $$2^{n/2}$$ queries.For beyond-birthday security, we focus on 6-round KAF. We prove that when the adjacent round-keys are independent, and independent round-functions are used, the 6 round KAF is secure up to $$2^{2n/3}$$ queries. To our knowledge, this is the first beyond-birthday security result for KAF without assuming completely independent round-keys.Our results hold in the multi-user setting as well, constituting the first non-trivial multi-user provable security results on Feistel ciphers. We finally demonstrate applications of our results on designing key-schedules and instantiating keyed sponge constructions.