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Applied Algebra, Algebraic Algorithms and Error-Correcting by Venkatesan Guruswami (auth.), Serdar Boztaş, Hsiao-Feng

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

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

The 33 revised complete papers awarded including 8 invited papers have been rigorously reviewed and chosen from sixty one submissions. one of the matters addressed are block codes, together with list-decoding algorithms; algebra and codes: jewelry, 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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This paper introduces inverted Edwards coordinates. Inverted Edwards coordinates (X1 : Y1 : Z1 ) represent the affine point (Z1 /X1 , Z1 /Y1 ) on an Edwards curve; for comparison, standard Edwards coordinates (X1 : Y1 : Z1 ) represent the affine point (X1 /Z1 , Y1 /Z1 ). This paper presents addition formulas for inverted Edwards coordinates using only 9M + 1S. The formulas are not complete but still are strongly unified. Dedicated doubling formulas use only 3M + 4S, and dedicated tripling formulas use only 9M + 4S.

ASIACRYPT 2007. LNCS, vol. 4833. ie Abstract. We will discuss two different but related topics. We first give a connection between the Fourier spectrum of Boolean functions and subspaces of skew-symmetric subspaces where each nonzero element has a lower bound on its rank. Secondly, we discuss some connections between bent and near-bent functions. 1 Introduction Let Vn denote any n-dimensional vector space over F2 . The Fourier transform of a function f : Vn −→ Vm is defined by f (a, b) := (−1) b,f (x) + a,x x∈Vn for a ∈ Vn and b ∈ Vm , b = 0.

We showed in [4] that, when curve parameters are chosen properly, the addition law is even complete: it works for all inputs, with no exceptional cases. Our fast addition formulas in [4] have the same features. See Section 2 of this paper for a more detailed review of Edwards curves. In [2], together with Birkner and Peters, we showed that tripling on Edwards curves could be performed using only 9M + 4S. We also analyzed the optimal combinations of additions, doublings, triplings, windowing methods, on-the-fly precomputations, curve shapes, and curve formulas, improving upon the analysis in [6] by Doche and Imbert.

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