By Gerasimos C. Meletiou, Arne Winterhof (auth.), Joachim von zur Gathen, José Luis Imaña, Çetin Kaya Koç (eds.)
This booklet constitutes the refereed court cases of the second one foreign Workshop at the mathematics of Finite Fields, WAIFI 2008, held in Siena, Italy, in July 2008.
The sixteen revised complete papers offered have been conscientiously reviewed and chosen from 34 submissions. The papers are equipped in topical sections on constructions in finite fields, effective finite box mathematics, effective implementation and architectures, type and development of mappings over finite fields, and codes and cryptography.
Read or Download Arithmetic of Finite Fields: 2nd International Workshop, WAIFI 2008 Siena, Italy, July 6-9, 2008 Proceedings PDF
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Additional resources for Arithmetic of Finite Fields: 2nd International Workshop, WAIFI 2008 Siena, Italy, July 6-9, 2008 Proceedings
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Shparlinski, I. ) 8th International Conference on Finite Fields and Applications, Contemporary Mathematics. American Mathematical Society (to appear) 3. : Low-cost solutions for preventing simple side-channel analysis: Side-channel atomicity. IEEE Transactions on Computers 53(6), 760–768 (2004) 4. : Sequences of numbers generated by addition in formal groups and new primality and factorization tests. Advances in Applied Mathematics 7(4), 385–434 (1986) 5. : A Course in Computational Algebraic Number Theory.
Moreover, as the inverse of a point on an elliptic curve can in most cases be obtained for free, we mainly analyze their signed variants [14,15]. Quite surprisingly, we find a number of settings where the right-to-left methods outperform the left-to-right methods. Our strategy is to make use of mixed coordinate systems but, unlike [6], we do this on binary methods for scalar multiplication. Such a strategy only reveals useful for the right-to-left methods because, as will become apparent later, the point addition routine and the point doubling routine may use different input/output coordinate systems.
Likewise, as we consider inversion-free formulæ, we require that the input and output points are given in projective coordinates. This allows the efficient computation of successive point multiplications. In other words, we do not assume a priori conditions on the Z-coordinate of input point P . In summary, we are interested in developing of a fast, compact and generalpurpose point multiplication algorithm. 1 Coordinate Systems In Jacobian coordinates, a (general) point addition requires 11M + 5S.