Journal of Mathematical Cryptology (Jun 2020)
Quasi-subfield Polynomials and the Elliptic Curve Discrete Logarithm Problem
Abstract
We initiate the study of a new class of polynomials which we call quasi-subfield polynomials. First, we show that this class of polynomials could lead to more efficient attacks for the elliptic curve discrete logarithm problem via the index calculus approach. Specifically, we use these polynomials to construct factor bases for the index calculus approach and we provide explicit complexity bounds. Next, we investigate the existence of quasi-subfield polynomials.
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