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

Machine Theory

By Çetin Kaya Koç, Sihem Mesnager, Erkay Savaş

This ebook constitutes the refereed court cases 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 provided have been conscientiously reviewed and chosen from 27 submissions. This workshop is a discussion board of mathematicians, machine scientists, engineers and physicists acting study on finite box mathematics, attracted to speaking the advances within the conception, purposes, and implementations of finite fields. The workshop might help to bridge the distance among the mathematical thought of finite fields and their hardware/software implementations and technical applications.

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Extra resources for Arithmetic of Finite Fields: 5th International Workshop, WAIFI 2014, Gebze, Turkey, September 27-28, 2014. Revised Selected Papers

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In this work, we have a prime , along with an N -by-N sparse matrix A defined over Z, and we want to solve the linear system Aw = 0 over Z/ Z. g. 32-bit integers). In fact, around 90 % of the non-zero coefficients are ±1. 28 H. Jeljeli The very first columns of A are relatively dense, then the column density decreases gradually. The row density does not change significantly. We denote by nNZ the number of non-zero elements in A. See Fig. 1 for a typical density plot of a matrix arising in an FFS computation.

Springer, Heidelberg (2011) 44 H. Jeljeli 20. : Scan primitives for GPU computing, pp. 97–106, August 2007 21. : Class number, a theory of factorization, and genera. In: 1969 Number Theory Institute (Proc. Sympos. , Vol. XX, State Univ. , 1969), pp. 415–440. I. (1971) 22. : Optimizations to nfs linear algebra. In:CADO Workshop on Integer Factorization. html 23. : Residue Arithmetic and Its Applications to Computer Technology. McGraw-Hill Book Company, New York (1967) 24. : Residue arithmetic a tutorial with examples.

14. : Implementing the tate pairing. R. ) ANTS 2002. 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 ).

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