By Kazumaro Aoki, Jens Franke, Thorsten Kleinjung, Arjen K. Lenstra, Dag Arne Osvik (auth.), Kaoru Kurosawa (eds.)
ASIACRYPT 2007 was once 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 overseas organization for Cryptologic examine (IACR), in cooperation with the knowledge safety examine (iSECURES) Lab of Swinburne collage of expertise (Sarawak Campus) and the Sarawak improvement Institute (SDI), and was once ?nancially supported through the Sarawak executive. the overall Chair used to be Raphael Phan and that i had the privilege of serving because the software Chair. The convention bought 223 submissions (from which one submission used to be withdrawn). every one paper was once reviewed through no less than 3 contributors of this system Committee, whereas submissions co-authored by means of a software Committee member have been reviewed through no less than ?ve contributors. (Each computing device member may put up at so much one paper.) Many top of the range papers have been submitted, yet as a result of rather small quantity which may be approved, many excellent papers needed to be rejected. After eleven weeks of reviewing, this system Committee chosen 33 papers for presentation (two papers have been merged). The lawsuits comprise the revised types of the authorised 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 resources 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
Then dx1 x2 y1 y2 = 1 and dx1 x2 y1 y2 = −1. Example: d = 121665/121666 is not a square in the ﬁeld k = Z/(2255 − 19). The Edwards addition law is deﬁned for all (x1 , y1 ), (x2 , y2 ) on the Edwards curve x2 + y 2 = 1 + dx2 y 2 over k, and corresponds to the standard addition law on “Curve25519,” the elliptic curve v 2 = u3 + 486662u2 + u over k. The point at ∞ on Curve25519 corresponds to the point (0, 1) on the Edwards curve; Faster Addition and Doubling on Elliptic Curves 35 the point (0, 0) on Curve25519 √ corresponds to (0, −1); any other point (u, v) on Curve25519 corresponds to ( 486664u/v, (u − 1)/(u + 1)); a sum of points on Curve25519 corresponds to a sum of points on the Edwards curve.
Some applications can take advantage of multiplying by a constant d, and some applications can choose curves where d is small, but other applications cannot. To cover both situations we separately tally the cost D of multiplying by a curve parameter; the reader can substitute D = 0, D = M, or anything in between. 8M, 0M). 8M, 0M). We do not claim that these approximations are valid for most applications. The order of entries in our tables can easily be aﬀected by small changes in the S/M ratio, the D/M ratio, etc.
Of course, we also include our own algorithms for Edwards curves. Chudnovsky and Chudnovsky also pointed out, in the case of Jacobian coordinates, that readdition of a point is less expensive than the ﬁrst addition. The addition formulas for (X1 : Y1 : Z1 ) + (X2 : Y2 : Z2 ) use 1M + 1S to compute Z22 and Z23 ; by caching Z22 and Z23 one can save 1M + 1S in computing any (X : Y : Z ) + (X2 : Y2 : Z2 ). We comment that similar savings are possible for Jacobi intersections and Jacobi quartics. (Rather than distinguishing readditions from initial additions, Chudnovsky and Chudnovsky reported speeds for addition and doubling of points represented as (X : Y : Z : Z 2 : Z 3 ).
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 by Kazumaro Aoki, Jens Franke, Thorsten Kleinjung, Arjen K. Lenstra, Dag Arne Osvik (auth.), Kaoru Kurosawa (eds.)