Cyril Bouvier

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We give details on solving the discrete logarithm problem in the 202-bit prime order subgroup of F × 2 809 using the Function Field Sieve algorithm (FFS). To our knowledge, this computation is the largest discrete logarithm computation so far in a binary field extension of prime degree. The Function Field Sieve is the traditional approach for solving these(More)
In this paper we prove some divisibility properties of the cardinal-ity of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method (ECM) for integer factorization. The ideas of the proofs help us to find new families of elliptic curves(More)
The security of most current public-key cryptosystems is based on the difficulty of finding discrete logarithms in large finite fields or factoring large integers. Most discrete logarithm and integer factoring algorithms, such as the Number Field Sieve (NFS) or the Function Field Sieve (FFS), can be described in 3 main steps: data collection, filtering and(More)
A nonhypotensive dose of endotoxin (Escherichia coli lipopolysaccharide, 250 micrograms kg-1 h-1) impaired both the pressor responsiveness to noradrenaline and its effects in reducing renal and hindquarter blood flow, measured using ultrasound Doppler flow probes. Platelet activating factor (PAF, 50 ng kg-1 h-1) similarly impaired pressor responsiveness to(More)
—This article presents algorithms that convert multiple precision integer or floating-point numbers from radix 2 to radix 10 (or to any radix b > 2). Those algorithms, based on the " scaled remainder tree " technique, use multiplications instead of divisions in their critical part. Both quadratic and subquadratic algorithms are detailed, with proofs of(More)
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