Arithmetic of Finite Fields: 5th International Workshop, by Çetin Kaya Koç, Sihem Mesnager, Erkay Savaş

By Çetin Kaya Koç, Sihem Mesnager, Erkay Savaş

This ebook constitutes the refereed lawsuits of the fifth overseas Workshop at the mathematics of Finite box, WAIFI 2014, held in Gebze, Turkey, in September 2014. The nine revised complete papers and forty three invited talks offered have been rigorously reviewed and chosen from 27 submissions. This workshop is a discussion board of mathematicians, machine scientists, engineers and physicists appearing examine on finite box mathematics, drawn to speaking the advances within the concept, functions, and implementations of finite fields. The workshop may help to bridge the distance among the mathematical idea of finite fields and their hardware/software implementations and technical functions.

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Additional resources for Arithmetic of Finite Fields: 5th International Workshop, WAIFI 2014, Gebze, Turkey, September 27-28, 2014. Revised Selected Papers (Lecture Notes in Computer Science)

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The Block Wiedemann algorithm [11] proposes to use m random vectors for x and n random vectors for y. The sequence of scalars is thus replaced by a sequence of m × n matrices and the numbers of iterations of the first and third steps become (N/n + N/m) and N/n, respectively. The n subsequences can be computed independently and in parallel. So, the block Wiedemann method allows to distribute the computation without an additional overhead [25]. 1 Linear Algebra of FFS for GF(2619 ) The matrix has 650 k rows and columns.

LNCS, vol. 2369, pp. 324–337. Springer, Heidelberg (2002) 15. : On the function field sieve and the impact of higher splitting probabilities. A. ) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 109–128. Springer, Heidelberg (2013) 16. : Solving a 6120-bit DLP on a desktop computer. , Lisonˇek, P. ) SAC 2013. LNCS, vol. 8282, pp. 136–152. Springer, Heidelberg (2014) 17. : Breaking ‘128-bit secure’ supersingular binary curves (or how to solve discrete logarithms in F24·1223 and F212·367 ). org/2014/119 18.

Y Definition 1. The symmetric bilinear complexity of the multiplication mA in A, is the lowest integer n, such that there exists: n linear forms (φ1 , . . , φn ) on A, along with n elements (w1 , . . wi i=1 1 Which will here always be considered associative, commutative and unitary. c Springer International Publishing Switzerland 2015 C ¸ . Ko¸ c et al. ): WAIFI 2014, LNCS 9061, pp. 45–60, 2015. 1007/978-3-319-16277-5 3 (2) 46 M. Rambaud This quantity2 will be noted μsym (A/K). Other complexity measures are possible, especially over the field F2 .

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