By David Kohel, Robert Rolland (ed.)

ISBN-10: 0821849557

ISBN-13: 9780821849552

**Read or Download Arithmetic, Geometry, Cryptography and Coding Theory 2009 PDF**

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**Extra info for Arithmetic, Geometry, Cryptography and Coding Theory 2009**

**Example text**

On a Xα = 22 q si et seulement si Tr ηu = 1. De plus, on a Tr u = 1. (2) Si e ∈ (k∗ )3 , alors Xα = 0 ou 22 q. Il existe y ∈ k tel que y 4 +y 3 +y 2 +y = e et Xα = 22 q si et seulement si Tr ηy = 0. D´ emonstration. Lorsque e = 1, d’une part, si Z est racine de P (x), alors Q(Z) = Tr(aZ 5 + cZ) et d’autre part, si Z est une racine de x5 P (x) + 1, alors Q(Z ) = Tr(aZ 5 + cZ ). Supposons que u soit un ´el´ement de k v´eriﬁant Tr u = 1 et (u2 + u)3 = e = On a alors a7 α7 (u5 + u) = u−1 + u−2 et −7 .

His algorithm is very eﬃcient on a certain family of elliptic curves, called Montgomery’s curves. In this case, the diﬀerential addition costs 4M + 2S and the doubling 2M + 2S + 1D where 1D is a multiplication by a constant. Brier and Joye’s adaptation requires 9M + 2S for an addition and 6M + 3S for a doubling. The complexity of this general algorithm is then n(15M + 5S) + 3M + S + I for a n-bit scalar, where I is a modular inversion in the ﬁeld Fp and 3M + S + I is the cost to recover the Y -coordinate at the end.

Lin, and M. Scott, Endomorphisms for faster elliptic curve cryptography on a large class of curves, EUROCRYPT 2009, LNCS 5479 (2009), 518–535. H. -E. Hamid, H. Choukri, D. Naccache, M. Tunstall, and C. org/2004/100. T. Izu and T. Takagi, A fast parallel elliptic curve multiplication resistant against side channel attacks, PKC 2002, LNCS 2274 (2002), 371–374. M. Joye and C. Tymen, Protections against diﬀerential analysis for elliptic curve cryptography, CHES 2001, LNCS 2162 (2001), 377–390. M. M.

### Arithmetic, Geometry, Cryptography and Coding Theory 2009 by David Kohel, Robert Rolland (ed.)

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