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

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 used to be the thirteenth ASIACRYPT convention, and used to be backed through the overseas organization for Cryptologic learn (IACR), in cooperation with the data defense examine (iSECURES) Lab of Swinburne collage of know-how (Sarawak Campus) and the Sarawak improvement Institute (SDI), and used to be ?nancially supported by means of 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 The convention obtained 223 submissions (from which one submission was once withdrawn). every one paper was once reviewed via at the very least 3 participants of this system Committee, whereas submissions co-authored by way of a application Committee member have been reviewed by means of at the least ?ve individuals. (Each computing device member may possibly post at so much one paper.) Many high quality papers have been submitted, yet as a result of quite small quantity that could be permitted, 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 include the revised models of the accredited papers. those revised papers weren't topic to editorial evaluate 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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Step 2 – Factor Base Extension. The extended factor base F consists of ideals of norm bounded by B Ln ( 13 , 3 89 ). We sieve on the algebraic side only, using each additional prime ideal that we want to add as a special-q. We ask for a single relation between this prime ideal and the smaller ones. Step 3 – Oracle Queries. We query the oracle for the e-th root of the numbers x − yP for each integers pair {x, y} encountered in steps 1 and 2. We also query for the e-th root of all prime numbers below B .

For each special-q ideal written as q, α − r , we isolated the integers x ∈ [−228 , 228 ] such that the added contribution of factor base ideals to the norm of the ideal (r + qx − α) exceeded 2145 (out of an order of magnitude just below 2200 ). This selection process isolated instantaneously11 circa 100 candidates of which around nineteen yielded relations. Considering the largest 20, 000 ideals in the factor base as special-q ideals, we obtained 380, 000 relations. The sieving step was distributed over twenty cpus and claimed a couple of hours.

Lange (c + y1 )/(c − y1 ) = u2 and v1 = 2cu1 /x1 = −2cu2 /x2 = −v2 so P1 = −P2 . In both cases P1 + P2 = ∞ = P3 . Assume from now on that (x3 , y3 ) = (0, c). If (x1 , y1 ) = (0, −c) then (x3 , y3 ) = (−x2 , −y2 ). Now (x2 , y2 ) = (0, −c) (since otherwise (x3 , y3 ) = (0, c)) and (x2 , y2 ) = (0, c) so x2 = 0. Thus P1 = (0, 0) and P2 = (u2 , v2 ) with u2 = (c+y2 )/(c−y2 ) and v2 = 2cu2 /x2 . The standard addition law says that (0, 0) + (u2 , v2 ) = (r3 , s3 ) where r3 = (1/e)(v2 /u2 )2 − (4/e − 2) − u2 = 1/u2 and s3 = (v2 /u2 )(−r3 ) = −v2 /u22 .

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