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 foreign 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 offered including 2 invited papers have been conscientiously reviewed and chosen from forty submissions. one of the matters addressed are block codes; algebra and codes: jewelry, fields, and AG codes; cryptography; sequences; deciphering algorithms; and algebra: structures 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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**Extra resources for Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium, AAECC-15, Toulouse, France, May 12–16, 2003 Proceedings**

**Sample text**

1) – resulting in a ( 16 23% 13 −1) speed improvement. The second advantage is that fewer memory resources are required since points are represented with triplets instead of quadruplets. 4 Conclusion This paper revisited the Jacobi model initially suggested in [12] as a means for preventing side-channel attacks. Using an (extended) form of the Jacobi quartic, we derived a uniﬁed addition formula for adding or doubling points with only 13 ﬁeld multiplications. This is the fastest known uniﬁed addition law for elliptic curves whose order is a multiple of 2.

Let Π be the function of (9), and let (A, +) = (GF(q)2t , +) and (B, +) = (GF(q), +). Then the authentication code of (4) provides at least log2 (q 2t−1 − q t−1 ) bits of secrecy protection. Furthermore, we have PI = 1 q−1 1 + t+1 , PS = . q q q Optimality of the Codes of Theorem 3 Clearly, PI = 1q + qq−1 t+1 does not meet the lower bound on PI given in Lemma 2. We now prove that it meets the bound on PI given in Lemma 1 asymptotically. Clearly, H(E) = log2 q 2t . We now compute H(E|M). Suppose that a message m = (m1 , m2 ) has been observed.

An algorithm for producing the isogeny is presented in [CM94]. 5 Application to Cryptography The basic operation of elliptic curve cryptosystems is the point multiplication: given a point P = (x1 , y1 ) ∈ E(K), one has to compute Q = [k]P = (xk , yk ) for some 1 ≤ k < ordE P . Assume that the deﬁnition ﬁeld is Fp where p is a large prime. We have seen in Sect. 2 that in this case an elliptic curve with parameter a = −3 yields a point multiplication substantially faster when working within projective coordinates.

### 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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