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A General Polynomial Sieve

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Abstract

An important component of the index calculus methods for finding discrete logarithms is the acquisition of smooth polynomial relations. Gordon and McCurley (1992) developed a sieve to aid in finding smooth Coppersmith polynomials for use in the index calculus method. We discuss their approach and some of the difficulties they found with their sieve. We present a new sieving method that can be applied to any affine subspace of polynomials over a finite field.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634, USA

    Shuhong Gao & Jason Howell

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  1. Shuhong Gao
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  2. Jason Howell
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Gao, S., Howell, J. A General Polynomial Sieve. Designs, Codes and Cryptography 18, 149–157 (1999). https://doi.org/10.1023/A:1008393304548

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