July 15, 2017

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 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.

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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

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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.

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