Laurent Imbert

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In this paper, we propose a efficient and secure point multiplication algorithm, based on double-base chains. This is achieved by taking advantage of the sparseness and the ternary nature of the socalled double-base number system (DBNS). The speed-ups are the results of fewer point additions and improved formulæ for point triplings and quadruplings in both(More)
We present the first implementation of RSA in the Residue Number System (RNS) which does not require any conversion, either from radix to RNS beforehand or RNS to radix afterward. Our solution is based on an optimized RNS version of Montgomery multiplication. Thanks to the RNS, the proposed algorithms are highly parallelizable and seem then well suited to(More)
We investigate the impact of larger digit sets on the length of Double-Base Number system (DBNS) expansions. We present a new representation system called extended DBNS whose expansions can be extremely sparse. When compared with double-base chains, the average length of extended DBNS expansions of integers of size in the range 200– 500 bits is(More)
We describe an algorithm for point multiplication on generic elliptic curves, based on a representation of the scalar as a sum of mixed powers of 2 and 3. The sparseness of this so-called double-base number system, combined with some efficient point tripling formulae, lead to efficient point multiplication algorithms for curves defined over both prime and(More)
In SAC 2003, J. Chung and A. Hasan introduced a new class of specific moduli for cryptography, called the more generalized Mersenne numbers, in reference to J. Solinas’ generalized Mersenne numbers proposed in 1999. This paper pursues the quest. The main idea is a new representation, called Modular Number System (MNS), which allows efficient implementation(More)
In this paper we show how the usage of Residue Number Systems (RNS) can easily be turned into a natural defense against many side-channel attacks (SCA). We introduce a Leak Resistant Arithmetic (LRA), and present its capacities to defeat timing, power (SPA, DPA) and electromagnetic (EMA) attacks. keywords: Side Channel Attacks, Residue Number Systems, RNS(More)
Single and double scalar multiplications are the most computational intensive operations in elliptic curve based cryptosystems. Improving the performance of these operations is generally achieved by means of integer recoding techniques, which aim at minimizing the scalars’ density of nonzero digits. The hybrid binary-ternary number system provides both(More)
We propose an improved implementation of the SHA-2 hash family, with minimal operator latency and reduced hardware requirements. We also propose a high frequency version at the cost of only two cycles of latency per message. Finally we present a multi-mode architecture able to perform either a SHA-384 or SHA-512 hash or to behave as two independent SHA-224(More)
Among the various arithmetic operations required in implementing public key cryptographic algorithms, the elliptic curve point multiplication has probably received the maximum attention from the research community in the last decade. Many methods for efficient and secure implementation of point multiplication have been proposed. The efficiency of these(More)
A recently introduced double-base number representation has proved to be successful in improving the performance of several algorithms in cryptography and digital signal processing. The index-calculus version of this number system can be regarded as a two-dimensional extension of the classical logarithmic number system. This paper builds on previous special(More)