Resistance to Timing Attacks for Sampling and Privacy Preserving Schemes

Side channel attacks, and in particular timing attacks, are a fundamental obstacle for secure implementation of algorithms and cryptographic protocols. These attacks and countermeasures have been widely researched for decades. We offer a new perspective on resistance to timing attacks. We focus on sampling algorithms and their application to differential privacy. We define sampling algorithms that do not reveal information about the sampled output through their running time. More specifically: (1) We characterize the distributions that can be sampled from in a "time oblivious" way, meaning that the running time does not leak any information about the output. We provide an optimal algorithm in terms of randomness used to sample for these distributions. We give an example of an efficient randomized algorithm ? such that there is no subexponential algorithm with the same output as ? that does not reveal information on the output or the input, therefore we show leaking information on either the input or the output is unavoidable. (2) We consider the impact of timing attacks on (pure) differential privacy mechanisms. It turns out that if the range of the mechanism is unbounded, such as counting, then any time oblivious pure DP mechanism must give a useless output with constant probability (the constant is mechanism dependent) and must have infinite expected running time. We show that up to this limitations it is possible to transform any pure DP mechanism into a time oblivious one

(Quantum) Collision Attacks on Reduced Simpira v2

Simpira v2 is an AES-based permutation proposed by Gueron and Mouha at ASIACRYPT 2016. In this paper, we build an improved MILP model to count the differential and linear active Sboxes for Simpira v2, which achieves tighter bounds of the minimum number of active Sboxes for a few versions of Simpira v2. Then, based on the new model, we find some new truncated differentials for Simpira v2 and give a series (quantum) collision attacks on two versions of reduced Simpira v2

Quantum Collision Attacks on AES-like Hashing with Low Quantum Random Access Memories

At EUROCRYPT 2020, Hosoyamada and Sasaki proposed the first dedicated quantum attack on hash functions --- a quantum version of the rebound attack exploiting differentials whose probabilities are too low to be useful in the classical setting. This work opens up a new perspective toward the security of hash functions against quantum attacks. In particular, it tells us that the search for differentials should not stop at the classical birthday bound. Despite these interesting and promising implications, the concrete attacks described by Hosoyamada and Sasaki make use of large quantum random access memories (qRAMs), a resource whose availability in the foreseeable future is controversial even in the quantum computation community. Without large qRAMs, these attacks incur significant increases in time complexities. In this work, we reduce or even avoid the use of qRAMs by performing a quantum rebound attack based on differentials with non-full-active super S-boxes. Along the way, an MILP-based method is proposed to systematically explore the search space of useful truncated differentials with respect to rebound attacks. As a result, we obtain improved attacks on AES-MMO, AES-MP, and the first classical collision attacks on 4- and 5-round Grostl-512. Interestingly, the use of non-full-active super S-box differentials in the analysis of AES-MMO gives rise to new difficulties in collecting enough starting points. To overcome this issue, we consider attacks involving two message blocks to gain more degrees of freedom, and we successfully compress the qRAM demand of the collision attacks on AES-MMO and AES-MP (EUROCRYPT 2020) from $2^{48}$ to a range from $2^{16}$ to $0$, while still maintaining a comparable time complexity. To the best of our knowledge, these are the first dedicated quantum attacks on hash functions that slightly outperform Chailloux, Naya-Plasencia, and Schrottenloher\u27s generic quantum collision attack (ASIACRYPT 2017) in a model where large qRAMs are not available. This work demonstrates again how a clever combination of classical cryptanalytic technique and quantum computation leads to improved attacks, and shows that the direction pointed out by Hosoyamada and Sasaki deserves further investigation

Fully Adaptive Schnorr Threshold Signatures

We prove adaptive security of a simple three-round threshold Schnorr signature scheme, which we call Sparkle. The standard notion of security for threshold signatures considers a static adversary – one who must declare which parties are corrupt at the beginning of the protocol. The stronger adaptive adversary can at any time corrupt parties and learn their state. This notion is natural and practical, yet not proven to be met by most schemes in the literature. In this paper, we demonstrate that Sparkle achieves several levels of security based on different corruption models and assumptions. To begin with, Sparkle is statically secure under minimal assumptions: the discrete logarithm assumption (DL) and the random oracle model (ROM). If an adaptive adversary corrupts fewer than t/2 out of a threshold of t + 1 signers, then Sparkle is adaptively secure under a weaker variant of the one-more discrete logarithm assumption (AOMDL) in the ROM. Finally, we prove that Sparkle achieves full adaptive security, with a corruption threshold of t, under AOMDL in the algebraic group model (AGM) with random oracles. Importantly, we show adaptive security without requiring secure erasures. Ours is the first proof achieving full adaptive security without exponential tightness loss for any threshold Schnorr signature scheme; moreover, the reduction is tight

How to Prove Schnorr Assuming Schnorr: Security of Multi- and Threshold Signatures

This work investigates efficient multi-party signature schemes in the discrete logarithm setting. We focus on a concurrent model, in which an arbitrary number of signing sessions may occur in parallel. Our primary contributions are: (1) a modular framework for proving the security of Schnorr multisignature and threshold signature schemes, (2) an optimization of the two-round threshold signature scheme $\mathsf{FROST}$ that we call $\mathsf{FROST2}$, and (3) the application of our framework to prove the security of $\mathsf{FROST2}$ as well as a range of other multi-party schemes. We begin by demonstrating that our framework is applicable to multisignatures. We prove the security of a variant of the two-round $\mathsf{MuSig2}$ scheme with proofs of possession and a three-round multisignature $\mathsf{SimpleMuSig}$. We introduce a novel three-round threshold signature $\mathsf{SimpleTSig}$ and propose an optimization to the two-round $\mathsf{FROST}$ threshold scheme that we call $\mathsf{FROST2}$. $\mathsf{FROST2}$ reduces the number of scalar multiplications required during signing from linear in the number of signers to constant. We apply our framework to prove the security of $\mathsf{FROST2}$ under the one-more discrete logarithm assumption and $\mathsf{SimpleTSig}$ under the discrete logarithm assumption in the programmable random oracle model

Triangulating Rebound Attack on AES-like Hashing

The rebound attack was introduced by Mendel et al. at FSE 2009 to fulfill a heavy middle round of a differential path for free, utilizing the degree of freedom from states. The inbound phase was extended to 2 rounds by the Super-Sbox technique invented by Lamberger et al. at ASIACRYPT 2009 and Gilbert and Peyrin at FSE 2010. In ASIACRYPT 2010, Sasaki et al. further reduced the requirement of memory by introducing the non-full-active Super-Sbox. In this paper, we further develop this line of research by introducing Super-Inbound, which is able to connect multiple 1-round or 2-round (non-full-active) Super-Sbox inbound phases by utilizing fully the degrees of freedom from both states and key, yet without the use of large memory. This essentially extends the inbound phase by up to 3 rounds. We applied this technique to find classic or quantum collisions on several AES-like hash functions, and improved the attacked round number by 1 to 5 in targets including AES-128 and SKINNY hashing modes, Saturnin-Hash, and Grostl-512. To demonstrate the correctness of our attacks, the semi-free-start collision on 6-round AES-128-MMO/MP with estimated time complexity $2^{24}$ in classical setting was implemented and an example pair was found instantly on a standard PC