Alexandre Duc

Making Masking Security Proofs Concrete - Or How to Evaluate the Security of any Leaking Device

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.

Unaligned rebound attack: application to keccak

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 2491.47. Our results have been implemented and verified experimentally on a small version of Keccak.

Better Algorithms for LWE and LWR

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.

HELEN: A Public-Key Cryptosystem Based on the LPN and the Decisional Minimal Distance Problems

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 Fujisaki-Okamoto 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.

TCHo: A Code-Based Cryptosystem

TCHo is a public-key cryptosystem based on the hardness of finding a multiple polynomial with low weight and on the hardness of distinguishing between the output of an LFSR with noise and some random source. An early version was proposed in 2006 by Finiasz and Vaudenay with non-polynomial (though practical) decryption time. The latest version came in 2007 with more co-authors. It reached competitive (heuristic) polynomial complexity and IND-CPA security. Since then, a key-recovery chosen ciphertext attack was published by Herrmann and Leander in 2009. In this paper we review the state of the art on this cryptosystem, together with some latest improvements regarding implementation and selection of parameters. We provide also more formal results regarding correctness and we update the key generation algorithm.

Making Masking Security Proofs Concrete (Or How to Evaluate the Security of Any Leaking Device), Extended Version

We investigate the relationship 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 the measurement complexity and the key enumeration time complexity in divide-and-conquer side-channel attacks and show that these complexities can be lower bounded based on the mutual information metric, using simple and efficient algorithms. The combination of these observations enables significant reductions of the evaluation costs for certification bodies.

Unifying Leakage Models: From Probing Attacks to Noisy Leakage

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.