An effective countermeasure against side-channel attacks is to mask all sensitive intermediate variables with one (or more) random value(s). When a cryptographic algorithm involves both arithmetic and Boolean operations, it is necessary to convert from arithmetic masking to Boolean masking and vice versa. At CHES 2001, Goubin introduced two algorithms for secure conversion between arithmetic and Boolean masks, but his approach can only be applied to first-order masking. In this paper, we present and evaluate new conversion algorithms that are secure against attacks of any order. To convert masks of a size of k bits securely against attacks of order n, the proposed algorithms have a time complexity of O(n 2 k) in both directions and are proven to be secure in the Ishai, Sahai, and Wagner (ISW) framework for private circuits. We evaluate our algorithms using HMAC-SHA-1 as example and report the execution times we achieved on a 32-bit AVR microcontroller.

Abstract. A general technique to protect a cryptographic algorithm against side-channel attacks consists in masking all intermediate variables with a random value. For cryptographic algorithms combining Boolean operations with arithmetic operations, one must then perform conversions between Boolean masking and arithmetic masking. At CHES 2001, Goubin described a very elegant algorithm for converting from Boolean masking to arithmetic masking, with only a constant number of operations. Goubin also described an algorithm for converting from arithmetic to Boolean masking, but with O(k) operations where k is the addition bit size. In this paper we describe an improved algorithm with time complexity O(log k) only. Our new algorithm is based on the Kogge-Stone carry look-ahead adder, which computes the carry signal in O(log k) instead of O(k) for the classical ripple carry adder. We also describe an algorithm for performing arithmetic addition modulo 2 k directly on Boolean shares, with the same complexity O(log k) instead of O(k). We prove the security of our new algorithm against first-order attacks. Our algorithm performs well in practice, as for k = 64 we obtain a 23% improvement compared to Goubin's algorithm. Our solution naturally extends to higher-order countermeasures with complexity O(n 2 · log k) instead of O(n 2 · k) for n shares.

Leakage-resilient cryptography aims to extend the rigorous guarantees achieved through the provable security paradigm to physical implementations. The constructions designed on basis of this new approach inevitably suffer from an Achilles heel: a bounded leakage assumption is needed. Currently, a huge gap exists between the theory of such designs and their implementation to confirm the leakage resilience in practice. The present work tries to narrow this gap for the leakage-resilient bilinear ElGamal key encapsulation mechanism (BEG-KEM) proposed by Kiltz and Pietrzak in 2010. Our first contribution is a variant of the bounded leakage and the only-computation-leaks model that is closer to practice. We weaken the restriction on the image size of the leakage functions in these models and only A preliminary version of this paper has appeared at PROOFS 2014. insist that the inputs to the leakage functions have sufficient min-entropy left, in spite of the leakage, with no limitation on the quantity of this leakage. We provide a novel security reduction for BEG-KEM in this relaxed leakage model using the generic bilinear group axiom. Secondly, we show that a naive implementation of the exponentiation in BEG-KEM makes it impossible to meet the leakage bound. Instead of trying to find an exponentiation algorithm that meets the leakage axiom (which is a non-trivial problem in practice), we propose an advanced scheme, BEG-KEM+, that avoids exponentiation by a secret value, but rather uses an encoding into the base group due to Fouque and Tibouchi. Thirdly, we present a software implementation of BEG-KEM+ based on the Miracl library and provide detailed experimental results. We also assess its (theoretical) resistance against power analysis attacks from a practical perspective, taking into account the state-of-the-art in side-channel cryptanalysis.

Abstract. To guarantee the security of a cryptographic implementation against Side Channel Attacks, a common approach is to formally prove the security of the corresponding scheme in a model as pertinent as possible. Nowadays, security proofs for masking schemes in the literature are usually conducted for models where only the manipulated data are assumed to leak. However in practice, the leakage is better modeled encompassing the memory transitions as e.g. the Hamming distance model. From this observation, a natural question is to decide at which extent a countermeasure proved to be secure in the first model stays secure in the second. In this paper, we look at this issue and we show that it must definitely be taken into account. Indeed, we show that a countermeasure proved to be secure against second-order side-channel attacks in the first model becomes vulnerable against a first-order side-channel attack in the second model. Our result emphasize the issue of porting an implementation from devices leaking only on the manipulated data to devices leaking on the memory transitions.

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