New PDF release: Applied Algebra, Algebraic Algorithms and Error-Correcting

By Jacques Stern (auth.), Marc Fossorier, Tom Høholdt, Alain Poli (eds.)

ISBN-10: 3540401113

ISBN-13: 9783540401117

ISBN-10: 3540448284

ISBN-13: 9783540448280

This publication constitutes the refereed court cases of the fifteenth overseas Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-15, held in Toulouse, France, in may well 2003.

The 25 revised complete papers awarded 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: structures in algebra, Galois teams, differential algebra, and polynomials.

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Additional resources for Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium, AAECC-15, Toulouse, France, May 12–16, 2003 Proceedings

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6 Concluding Remarks The first two constructions of this paper are specific, while the third construction is generic in the sense that any perfect nonlinear mapping may be employed to obtain authentication codes with secrecy. Thus new functions with perfect nonlinearity give new authentication/secrecy codes. Note that authentication codes with secrecy have six parameters. It is in general hard to compare two classes of them. We have not found any existing class of authentication codes that could be compared with those presented in this paper.

In order to make easier point compression/decompression, elliptic curve cryptosystems are usually defined over Fp with p ≡ 3 (mod 4). In that case, all elliptic curves that can be rescaled to a = −3c2 can also be rescaled to a = −3, independently of the value of c. 4 Isogenies An isogeny between two elliptic curves E and E defined over K is a nonconstant2 morphism φ : E → E . The degree of isogeny φ is defined to be deg φ = [K(E) : φ∗ K(E )] where φ∗ : K(E ) → K(E), f → φ∗ (f ) = f ◦ φ denotes the map induced by φ.

Letting ξ a square-root of the corresponding square ±(θ2 − θ3 ), it follows that = ξ 4 /16 = (ξ/2)4 . If p ≡ 1 (mod 4) then there is a 1/8 chance that we cannot find a pair of indices such that (θi − θj ) is a square modulo p. If such a pair exists, we let ξ denote the corresponding square-root and again, after 40 O. Billet and M. Joye a possible re-arrangement, we get = (ξ/2)4 . The change of variable X ← 2X/ξ then transforms the previous quartic into Y 2 = X 4 − 2ρ X 2 Z 2 + Z 4 (13) where ρ = 4δ/ξ 2 .

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium, AAECC-15, Toulouse, France, May 12–16, 2003 Proceedings by Jacques Stern (auth.), Marc Fossorier, Tom Høholdt, Alain Poli (eds.)


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