By Henning Stichtenoth (auth.), M. Anwar Hasan, Tor Helleseth (eds.)
This booklet constitutes the refereed court cases of the 3rd foreign 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 equipped in topical sections on effective finite box mathematics, pseudo-random numbers and sequences, Boolean features, services, Equations and modular multiplication, finite box mathematics for pairing established cryptography, and finite box, cryptography and coding.
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Additional info for Arithmetic of Finite Fields: Third International Workshop, WAIFI 2010, Istanbul, Turkey, June 27-30, 2010. Proceedings
C1 , c0 ), each ci is a 32-bit word, and 0 ≤ c < p2521 . Output: Integer d ≡ c mod p521 . Deﬁne 521-bit integers: s1 = (c16 , . . , c1 , c0 ), s2 = (c32 , . . ca Abstract. Gaussian normal bases have been included in a number of standards, such as IEEE  and NIST  for elliptic curve digital signature algorithm (ECDSA). Among diﬀerent ﬁnite ﬁeld operations used in this algorithm, multiplication is the main operation. In this paper, we consider type T Gaussian normal basis (GNB) multipliers over GF (2m ), where m is odd.
The complexity reduction algorithm to reduce the number of XOR gates in the block ρ of Figure 2 is summarized as follows. Input: The multiplication matrix M and digit size d for type T GNB over GF (2m ). Output: A pairset which contains all the pairs that should be implemented in the block ρ1 . This set will be used to obtain the formulations for the implementation of the modiﬁed multiplier. 1. Corresponding to the output signals of the P block in Figure 1, an m−1 2 m−1 2 ×T matrix denoted by μ = [μk ]k=1 is constructed, where μk is the row k, 1 ≤ k ≤ m−1 of the matrix μ.
The conventional wisdom for many years was that type-I normal bases were a unique exception. For all other normal bases the best multiplication methods in the literature were quite slow. In particular, multiplication in a “type-II optimal normal basis” of F2n was asymptotically at least twice as expensive as multiplication in traditional low-weight polynomial bases (trinomial bases and pentanomial bases): • Traditional normal-basis multipliers use Θ(n2 ) bit operations. • The type-II multiplier in [FH07] uses approximately 13 · 3 log2 n bit operations.