Applied Algebra, Algebraic Algorithms and Error-Correcting - download pdf or read online

By Venkatesan Guruswami (auth.), Serdar Boztaş, Hsiao-Feng (Francis) Lu (eds.)

ISBN-10: 3540772235

ISBN-13: 9783540772231

ISBN-10: 3540772243

ISBN-13: 9783540772248

This booklet constitutes the refereed lawsuits of the seventeenth foreign Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-17, held in Bangalore, India, in December 2007.

The 33 revised complete papers provided including 8 invited papers have been rigorously reviewed and chosen from sixty one submissions. one of the topics addressed are block codes, together with list-decoding algorithms; algebra and codes: earrings, fields, algebraic geometry codes; algebra: jewelry and fields, polynomials, variations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.

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Extra resources for Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 17th International Symposium, AAECC-17, Bangalore, India, December 16-20, 2007. Proceedings

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Research supported by the Claude Shannon Institute, Science Foundation Ireland Grant 06/MI/006. S. F. ): AAECC 2007, LNCS 4851, pp. 28–37, 2007. c Springer-Verlag Berlin Heidelberg 2007 Spectra of Boolean Functions, Subspaces of Matrices 29 For a function f : L −→ L the formula for f becomes (−1)tr(bf (x)+ax) . f (a, b) := (1) x∈L In this context, f is almost bent if and only if each of the Boolean functions tr(bf (x)) is near-bent, for all b ∈ L, b = 0. If f is a monomial permutation, say f (x) = xd where (d, 2n − 1) = 1, then f is almost bent if and only if tr(f (x)) is near-bent.

Specifically, Q(X, Y ) was restricted to have a non-trivially bounded (1, k)-weighted degree. The (1, k)-weighted degree of a monomial X i Y j is i + jk and the (1, k)-weighted degree of a bivariate polynomial Q(X, Y ) is the maximum (1, k)-weighted degree among its monomials. The intuition behind defining such a weighted degree is that given Q(X, Y ) with weighted (1, k) degree of D, the univariate polynomial Q(X, f (X)), where f (X) is some degree k polynomial, has total degree at most D. The upper bound D is chosen carefully such that if f (X) is a codeword that needs to be output, then Q(X, f (X)) has more than D zeroes and thus Q(X, f (X)) ≡ 0, which in √ turn implies that Y − f (X) divides Q(X, Y ).

Springer, Heidelberg (2006) 2. : Optimizing Double-Base Elliptic-Curve Single-Scalar Multiplication. , Yung, M. ) INDOCRYPT 2007. LNCS, vol. 4859, pp. 167–182. Springer, Heidelberg (2007) 3. org/EFD 4. : Faster Addition and Doubling on Elliptic Curves. In: Kurosawa, K. ) ASIACRYPT 2007. LNCS, vol. 4833, pp. 29–50. to/newelliptic/ 5. : Complete Systems of Two Addition Laws for Elliptic Curves. J. Number Theory 53, 229–240 (1995) 6. : Extended Double-Base Number System with Applications to Elliptic Curve Cryptography.

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 17th International Symposium, AAECC-17, Bangalore, India, December 16-20, 2007. Proceedings by Venkatesan Guruswami (auth.), Serdar Boztaş, Hsiao-Feng (Francis) Lu (eds.)

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