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ÐThis paper deals with the computation of reciprocals, square roots, inverse square roots, and some elementary functions using small tables, small multipliers, and, for some functions, a final ªlargeº (almost full-length) multiplication. We propose a method, based on argument reduction and series expansion, that allows fast evaluation of these functions in(More)
—The Table Maker's Dilemma is the problem of always getting correctly rounded results when computing the elementary functions. After a brief presentation of this problem, we present new developments that have helped us to solve this problem for the double-precision exponential function in a small domain. These new results show that this problem can be(More)
There has been a lot of interest in recent years in the problems faced by cryptosystems due to side channel attacks. Algorithms for elliptic curve point scalar multiplication such as the double and add method are prone to such attacks. By making use of special addition chains, it is possible to implement a simple power analysis (SPA) resistant cryptosystem.(More)
—A unified view of most previous table-lookup-and-addition methods (bipartite tables, SBTM, STAM, and multipartite methods) is presented. This unified view allows a more accurate computation of the error entailed by these methods, which enables a wider design space exploration, leading to tables smaller than the best previously published ones by up to 50(More)
This paper presents an unified view of most previous table-lookup-and-addition methods: bipartite tables, SBTM, STAM and multipartite method. This new definition allows a more accurate computation of the error entailed by these methods. Being more general, it also allows an exhaustive design space exploration which has been implemented, and leads to tables(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)
The Table Maker's Dilemma is the problem of always getting correctly rounded results when computing the elementary functions. After a brief presentation of this problem, we present new developments that have helped us to solve this problem for the double-precision exponential function in a small domain. These new results show that this problem can be(More)
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion(More)
This paper presents some improvements on the optimization of hardware multiplication by constant matrices. We focus on the automatic generation of circuits that involve constant matrix multiplication (CMM), i.e. multiplication of a vector by a constant matrix. The proposed method, based on number recoding and dedicated common sub-expression factorization(More)