Download Advances in Cryptology – ASIACRYPT 2007: 13th International by Kazumaro Aoki, Jens Franke, Thorsten Kleinjung, Arjen K. PDF

By Kazumaro Aoki, Jens Franke, Thorsten Kleinjung, Arjen K. Lenstra, Dag Arne Osvik (auth.), Kaoru Kurosawa (eds.)

ASIACRYPT 2007 used to be held in Kuching, Sarawak, Malaysia, in the course of December 2–6, 2007. This was once the thirteenth ASIACRYPT convention, and was once backed by way of the foreign organization for Cryptologic learn (IACR), in cooperation with the knowledge safeguard study (iSECURES) Lab of Swinburne collage of know-how (Sarawak Campus) and the Sarawak improvement Institute (SDI), and was once ?nancially supported via the Sarawak govt. the overall Chair used to be Raphael Phan and that i had the privilege of serving because the application Chair. The convention bought 223 submissions (from which one submission used to be withdrawn). every one paper used to be reviewed by way of no less than 3 individuals of this system Committee, whereas submissions co-authored via a software Committee member have been reviewed through at the very least ?ve individuals. (Each laptop member may put up at such a lot one paper.) Many top quality papers have been submitted, yet because of the quite small quantity which can be authorized, many first-class papers needed to be rejected. After eleven weeks of reviewing, this system Committee chosen 33 papers for presentation (two papers have been merged). The complaints comprise the revised types of the authorized papers. those revised papers weren't topic to editorial evaluation and the authors undergo complete accountability for his or her contents.

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Additional info for Advances in Cryptology – ASIACRYPT 2007: 13th International Conference on the Theory and Application of Cryptology and Information Security, Kuching, Malaysia, December 2-6, 2007. Proceedings

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Org Abstract. Edwards recently introduced a new normal form for elliptic curves. Every elliptic curve over a non-binary field is birationally equivalent to a curve in Edwards form over an extension of the field, and in many cases over the original field. This paper presents fast explicit formulas (and register allocations) for group operations on an Edwards curve. , 3 field multiplications and 4 field squarings. If curve parameters are chosen to be small then the algorithm for mixed addition uses only 9M + 1S and the algorithm for non-mixed addition uses only 10M + 1S.

We first set up on the algebraic side a number field K = Q(α) defined by a polynomial equation f (α) = 0. The easiest (though not unique) choice for the second side is a rational side given by a polynomial g such that f and g share a common root P modulo n. The classical base-m technique can be used for this purpose. We denote by ρ the rational root of g (we have ρ = m if g is monic). 22 A. Joux, D. Naccache, and E. Thom´e Step 1 – Precomputation. The factor base F on the algebraic side consists of ideals of norm bounded by B Ln ( 13 , 3 pairs {x, y} yielding relations of the form: (x − yα) = p mp , 4 9 ).

Miller, in his Crypto ’85 paper introducing elliptic-curve cryptography, proposed carrying out these operations on points represented in Jacobian form: “Each point is represented by the triple (x, y, z) which corresponds to the point (x/z 2 , y/z 3)” on a curve y 2 = x3 + a4 x + a6 . See [37, page 424]. One can add two points using 16 field multiplications, specifically 11M + 5S, with the fastest algorithms known today; here we keep separate tallies of squarings S and general multiplications M. A mixed addition — this means that one input has z = 1 — takes only 7M + 4S.

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