Arithmetic of Finite Fields: Third International Workshop, by Henning Stichtenoth (auth.), M. Anwar Hasan, Tor Helleseth

By Henning Stichtenoth (auth.), M. Anwar Hasan, Tor Helleseth (eds.)

This e-book constitutes the refereed lawsuits of the 3rd overseas Workshop at the mathematics of Finite Fields, WAIFI 2010, held in Istanbul, Turkey, in June 2010. The 15 revised complete papers awarded have been rigorously reviewed and chosen from 33 submissions. The papers are geared up in topical sections on effective finite box mathematics, pseudo-random numbers and sequences, Boolean capabilities, capabilities, Equations and modular multiplication, finite box mathematics for pairing dependent cryptography, and finite box, cryptography and coding.

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Extra info for Arithmetic of Finite Fields: Third International Workshop, WAIFI 2010, Istanbul, Turkey, June 27-30, 2010. Proceedings

Example text

At the time of this writing, the latest version of [BBB+ 09] reports the speed of software that extends the synergy of [Ber09a] to include type-II bases, using Shokrollahi’s approach together with the improvements described in Section 3 of this paper. The latest GPU software incorporates additional improvements described in subsequent sections of this paper. A very recent pipelined FPGA implementation of the ECC2K-130 computation also uses this approach and is much faster than previous FPGA implementations; see [FBB+ 10].

It has been known Permanent ID of this document: 90995f3542ee40458366015df5f2b9de. 12. This work has been supported in part by the European Commission through the ICT Programme under Contract ICT–2007–216676 ECRYPT-II and in part by the National Science Foundation under grant ITR–0716498. A. Hasan and T. ): WAIFI 2010, LNCS 6087, pp. 41–61, 2010. J. Bernstein and T. Lange for many years that this basis allows not only fast repeated squarings but also surprisingly fast multiplications, costing only M (n)+2n−2 bit operations where M (n) is the minimum cost of multiplying n-coefficient polynomials.

C1 , c0 ), each ci is a 32-bit word, and 0 ≤ c < p2384 . Output: Integer d ≡ c mod p384 . Define 384-bit integers: s1 = ( c11 , c10 , c9 , c8 , c7 , c6 , c5 , c4 , c3 , c2 , c1 , c0 ), s2 = ( 0, 0, 0, 0, 0, c23 , c22 , c21 , 0, 0, 0, 0), s3 = ( c23 , c22 , c21 , c20 , c19 , c18 , c17 , c16 , c15 , c14 , c13 , c12 ), s4 = ( c20 , c19 , c18 , c17 , c16 , c15 , c14 , c13 , c12 , c23 , c22 , c21 ), s5 = ( c19 , c18 , c17 , c16 , c15 , c14 , c13 , c12 , c20 , 0, c23 , 0), s6 = ( 0, 0, 0, 0, c23 , c22 , c21 , c20 , 0, 0, 0, 0), s7 = ( 0, 0, 0, 0, 0, 0, c23 , c22 , c21 , 0, 0, c20 ), s8 = ( c22 , c21 , c20 , c19 , c18 , c17 , c16 , c15 , c14 , c13 , c12 , c23 ), s9 = ( 0, 0, 0, 0, 0, 0, 0, c23 , c22 , c21 , c20 , 0), s10 = ( 0, 0, 0, 0, 0, 0, 0, c23 , c23 , 0, 0, 0); return (d = s1 + 2s2 + s3 + s4 + s5 + s6 + s7 − s8 − s9 − s10 ); Algorithm 9.

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