Download Applied Algebra, Algebraic Algorithms and Error-Correcting by Jacques Stern (auth.), Marc Fossorier, Tom Høholdt, Alain PDF
By Jacques Stern (auth.), Marc Fossorier, Tom Høholdt, Alain Poli (eds.)
This publication constitutes the refereed lawsuits of the fifteenth overseas Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-15, held in Toulouse, France, in may possibly 2003.
The 25 revised complete papers provided including 2 invited papers have been rigorously reviewed and chosen from forty submissions. one of the topics addressed are block codes; algebra and codes: earrings, fields, and AG codes; cryptography; sequences; deciphering algorithms; and algebra: buildings in algebra, Galois teams, differential algebra, and polynomials.
Read or Download Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium, AAECC-15, Toulouse, France, May 12–16, 2003 Proceedings PDF
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Additional info for Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium, AAECC-15, Toulouse, France, May 12–16, 2003 Proceedings
Simmons, Authentication theory/coding theory, Advances in Cryptology – Crypto’ 84, Lecture Notes in Comput. , Vol. 196 (1984), 411–431. 14. R. Stinson, A construction for authentication/secrecy codes from certain combinatorial designs, J. Cryptography 1 (1988), 119–127. 15. R. Stinson and L. Teirlinck, A construction for authentication/secrecy codes from 3-homogeneous permutation groups, European J. Combin. 11 (1990), 73–79. The Jacobi Model of an Elliptic Curve and Side-Channel Analysis Olivier Billet1,2 and Marc Joye1 1 Gemplus Card International, Card Security Group La Vigie, Av.
2 Our Results Building on , we consider the Jacobi form not as the intersection of two quadrics but as a quartic. This allows points to be represented with triplets instead of quadruplets. Furthermore, this considerably reduces the number of required (ﬁeld) multiplications. As a result, we obtain the most eﬃcient (memorywise and computation-wise) uniﬁed formula for adding points on an elliptic curve whose order is a multiple of 2 (as required for OK-ECDH  or OK-ECDSA ). In particular, compared to , we get a 23% speed-up improvement with fewer memory requirements.
G. [3,11]. Initially, the discrete logarithm and the Diﬃe–Hellman mapping were suggested for use in practice for the multiplicative group of a ﬁnite ﬁeld. Recently, several lower bounds on the complexity of functions representing the discrete logarithm or the Diﬃe–Hellman mapping in ﬁnite ﬁelds have been obtained (e. g. [4,15]), including lower bounds on the degree of interpolation polynomials of functions related to the discrete logarithm or Diﬃe– Hellman mapping. Subexponential algorithms for solving the discrete logarithm problem in ﬁnite ﬁelds are known (see e.