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

This ebook 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 might 2003.

The 25 revised complete papers offered including 2 invited papers have been rigorously reviewed and chosen from forty submissions. one of the matters 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.

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

**Sample text**

Smart. Explicit 4-descents on an elliptic curve. , 77(4):385–404, 1996. 14. Joseph H. Silverman. The arithmetic of elliptic curves, volume 106 of Graduate Texts in Mathematics. Springer-Verlag, 1986. 15. T. N. Watson. A course of modern analysis. Cambridge University Press, 4th edition, 1927. , the group order has a cofactor ≤ 4) over Fp . This example is adapted from [12]. Let p = 2192 − 264 − 1. Over Fp , consider the Weierstraß elliptic curve E given by E/Fp : y 2 = x3 − 3x + b (∪ {O}) (14) where b = 5785156510951660859948362664535565676137370865272662811849.

This example is adapted from [12]. Let p = 2192 − 264 − 1. Over Fp , consider the Weierstraß elliptic curve E given by E/Fp : y 2 = x3 − 3x + b (∪ {O}) (14) where b = 5785156510951660859948362664535565676137370865272662811849. The order of E is four times a prime: #E = 4 · 1569275433846670190958947355830249374250393459078477724241 . The three points of order 2 on the Weierstraß curve are (θi , 0) with θ1 = 393113410321492593759236174468396523987365130802013387956 θ2 = 3722240065524459449962883383651126589463273788373166826730 .

3 Preventing SPA-Like Attacks We consider slightly more general quartics than those originally considered by Jacobi. Namely, we investigate quartics given by y 2 = x4 − 2δ x2 + 1 . ) Remarkably, all elliptic curves with a point of order 2 can be expressed by a quartic equation of the form of Eq. (7). Let E denote an elliptic curve (over K)2 given by a Weierstraß equation y 2 = x3 + ax + b with its point ‘at inﬁnity’ O. Suppose that E has a point of order 2, say, (θ, 0) ∈ E(K). Then, the above Weierstraß elliptic curve is birationnally equivalent to the (extended) Jacobi quartic Y 2 = X 4 − 2δ X 2 Z 2 + Z 4 2 Remember that we assume Char K = 2, 3.