No abstract

A recent trend in cryptography is to formally show the leakage resilience of cryptographic implementations in a given leakage model. One of the most prominent leakage model-the so-called bounded leakage model-assumes that the amount of leakage that an adversary receives is a-priori bounded. Unfortunately, it has been pointed out by several works that the assumption of bounded leakages is hard to verify in practice. A more realistic assumption is to consider that leakages are sufficiently noisy, following the engineering observation that real-world physical leakages are inherently perturbed by physical noise. While already the seminal work of Chari et al. (in: CRYPTO, pp 398-412, 1999) study security of side-channel countermeasures in the noisy model, only recently Prouff and Rivain (in: Johansson T, Nguyen PQ (eds) EUROCRYPT, volume 7881 of lecture notes in 931 computer science, pp 142-159, Springer, 2013) offer a full formal analysis of the masking countermeasure in a physically motivated noise model. In particular, the authors show that a block-cipher implementation that uses the Boolean masking scheme is secure against a very general class of noisy leakage functions. While this is an important step toward better understanding the security of masking schemes, the analysis of Prouff and Rivain has several shortcomings including in particular requiring leak-free gates. In this work, we provide an alternative security proof in the same noise model that overcomes these challenges. We achieve this goal by a new reduction from noisy leakage to the important model of probing adversaries (Ishai et al. in: CRYPTO, pp 463-481, 2003). This reduction is the main technical contribution of our work that significantly simplifies the formal security analysis of masking schemes against realistic side-channel leakages.

Abstract. The Learning With Error problem (LWE) is becoming more and more used in cryptography, for instance, in the design of some fully homomorphic encryption schemes. It is thus of primordial importance to find the best algorithms that might solve this problem so that concrete parameters can be proposed. The BKW algorithm was proposed by Blum et al. as an algorithm to solve the Learning Parity with Noise problem (LPN), a subproblem of LWE. This algorithm was then adapted to LWE by Albrecht et al. In this paper, we improve the algorithm proposed by Albrecht et al. by using multidimensional Fourier transforms. Our algorithm is, to the best of our knowledge, the fastest LWE solving algorithm. Compared to the work of Albrecht et al. we greatly simplify the analysis, getting rid of integrals which were hard to evaluate in the final complexity. We also remove some heuristics on rounded Gaussians. Some of our results on rounded Gaussians might be of independent interest. Moreover, we also analyze algorithms solving LWE with discrete Gaussian noise. Finally, we apply the same algorithm to the Learning With Rounding problem (LWR) for prime q, a deterministic counterpart to LWE. This problem is getting more and more attention and is used, for instance, to design pseudorandom functions. To the best of our knowledge, our algorithm is the first algorithm applied directly to LWR. Furthermore, the analysis of LWR contains some technical results of independent interest.

Abstract. We analyze the internal permutations of Keccak, one of the NIST SHA-3 competition finalists, in regard to differential properties. By carefully studying the elements composing those permutations, we are able to derive most of the best known differential paths for up to 5 rounds. We use these differential paths in a rebound attack setting and adapt this powerful freedom degrees utilization in order to derive distinguishers for up to 8 rounds of the internal permutations of the submitted version of Keccak. The complexity of the 8 round distinguisher is 2 491.47 . Our results have been implemented and verified experimentally on a small version of Keccak. This is currently the best known differential attack against the internal permutations of Keccak.

Abstract. We prove that if one can predict any of the bits of the input to an elliptic curve based one-way function over a finite field, then we can invert the function. In particular, our result implies that if one can predict any of the bits of the input to a classical pairing-based one-way function with non-negligible advantage over a random guess then one can efficiently invert this function and thus, solve the Fixed Argument Pairing Inversion problem (FAPI-1/FAPI-2). The latter has implications on the security of various pairing-based schemes such as the identity-based encryption scheme of BonehFranklin, Hess' identity-based signature scheme, as well as Joux's three-party one-round key agreement protocol. Moreover, if one can solve FAPI-1 and FAPI-2 in polynomial time then one can solve the Computational Diffie-Hellman problem (CDH) in polynomial time.Our result implies that all the bits of the functions defined above are hard-to-compute assuming these functions are one-way. The argument is based on a list-decoding technique via discrete Fourier transforms due to Akavia-Goldwasser-Safra as well as an idea due to Boneh-Shparlinski.

Abstract. A recent trend in cryptography is to formally show the leakage resilience of cryptographic implementations in a given leakage model. One of the most prominent leakage modelsthe so-called bounded leakage model -assumes that the amount of leakage is a-priori bounded. Unfortunately, it has been pointed out that the assumption of bounded leakages is hard to verify in practice. A more realistic assumption is to assume that leakages are sufficiently noisy, following the engineering observation that real-world physical leakages are inherently noisy. While the noisy leakage assumption has first been studied in the seminal work of Chari et al. (CRYPTO 99), the recent work of Prouff and Rivain (Eurocrypt 2013) provides the first analysis of a full masking scheme under a physically motivated noise model. In particular, the authors show that a block-cipher implementation that uses an additive masking scheme is secure against noisy leakages. Unfortunately, the security analysis of Prouff and Rivain has three important shortcomings: (1) it requires leak-free gates, (2) it considers a restricted adversarial model (random message attacks), and (3) the security proof has limited application for cryptographic settings. In this work, we provide an alternative security proof in the same noisy model that overcomes these three challenges. We achieve this goal by a new reduction from noisy leakage to the important theoretical model of probing adversaries (Ishai et al -CRYPTO 2003). Our work can be viewed as a next step of closing the gap between theory and practice in leakage resilient cryptography: while our security proofs heavily rely on concepts of theoretical cryptography, we solve problems in practically motivated leakage models.

Abstract. We propose HELEN, a code-based public-key cryptosystem whose security is based on the hardness of the Learning from Parity with Noise problem (LPN) and the decisional minimum distance problem. We show that the resulting cryptosystem achieves indistinguishability under chosen plaintext attacks (IND-CPA security). Using the FujisakiOkamoto generic construction, HELEN achieves IND-CCA security in the random oracle model. Our cryptosystem looks like the Alekhnovich cryptosystem. However, we carefully study its complexity and we further propose concrete optimized parameters.

Abstract. We investigate the relationships between theoretical studies of leaking cryptographic devices and concrete security evaluations with standard side-channel attacks. Our contributions are in four parts. First, we connect the formal analysis of the masking countermeasure proposed by Duc et al. (Eurocrypt 2014) with the Eurocrypt 2009 evaluation framework for side-channel key recovery attacks. In particular, we re-state their main proof for the masking countermeasure based on a mutual information metric, which is frequently used in concrete physical security evaluations. Second, we discuss the tightness of the Eurocrypt 2014 bounds based on experimental case studies. This allows us to conjecture a simplified link between the mutual information metric and the success rate of a side-channel adversary, ignoring technical parameters and proof artifacts. Third, we introduce heuristic (yet well-motivated) tools for the evaluation of the masking countermeasure when its independent leakage assumption is not perfectly fulfilled, as it is frequently encountered in practice. Thanks to these tools, we argue that masking with non-independent leakages may provide improved security levels in certain scenarios. Eventually, we consider the tradeoff between measurement complexity and key enumeration in divide-and-conquer side-channel attacks, and show that it can be predicted based on the mutual information metric, by solving a non-linear integer programming problem for which efficient solutions exist. The combination of these observations enables significant reductions of the evaluation costs for certification bodies.