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On the cubic sieve method for computing discrete logarithms over prime fields

Das, Abhijit and Madhavan, Veni CE (2005) On the cubic sieve method for computing discrete logarithms over prime fields. In: International Journal of Computer Mathematics, 82 (12). pp. 1481-1495.

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Abstract

In this paper, we report efficient implementations of the linear sieve and the cubic sieve methods for computing discrete logarithms over prime fields. We demonstrate through empirical performance measures that for a special class of primes the cubic sieve method runs about two times faster than the linear sieve method even in cases of small prime fields of the size about 150 bits. We also provide a heuristic estimate of the number of solutions of the congruence $X^{3}?=?Y^{2}Z$ (mod p) that is of central importance in the cubic sieve method.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to Taylor & Francis Ltd.
Keywords: Cryptography; Cryptanalysis; Finite field; Discrete logarithm; Sieve method
Department/Centre: Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)
Date Deposited: 01 Mar 2006
Last Modified: 19 Sep 2010 04:24
URI: http://eprints.iisc.ernet.in/id/eprint/5754

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