Cryptology ePrint Archive: Report 2004/153

A double large prime variation for small genus hyperelliptic index calculus

P. Gaudry and E. Thomé and N. Thériault and C. Diem

Abstract: In this article, we examine how the index calculus approach for computing discrete logarithms in small genus hyperelliptic curves can be improved by introducing a double large prime variation. Two algorithms are presented. The first algorithm is a rather natural adaptation of the double large prime variation to the intended context. On heuristic and experimental grounds, it seems to perform quite well but lacks a complete and precise analysis. Our second algorithm is a considerably simplified variant, which can be analyzed easily. The resulting complexity improves on the fastest known algorithms. Computer experiments show that for hyperelliptic curves of genus three, our first algorithm surpasses Pollard's Rho method even for rather small field sizes.

Category / Keywords: public-key cryptography / discrete logarithm problem, hyperelliptic curves, index calculus

Date: received 4 Jul 2004, last revised 21 Nov 2005

Contact author: gaudry at lix polytechnique fr

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Note: The paper now contains a complete proof of our result without any assumption or heuristic. Claus Diem is added as a co-author.

Version: 20051121:174602 (All versions of this report)

Short URL: ia.cr/2004/153