Cryptology ePrint Archive: Report 2013/707

A reduction of Semigroup DLP to classic DLP

Matan Banin and Boaz Tsaban

Abstract: We present a polynomial-time reduction of the discrete logarithm problem in any periodic (or torsion) semigroup (SGDLP) to the classic DLP in a _subgroup_ of the same semigroup. It follows that SGDLP can be solved in polynomial time by quantum computers, and that SGDLP has subexponential complexity whenever the classic DLP in the corresponding groups has subexponential complexity. We also consider several natural constructions of nonperiodic semigroups, and provide polynomial time solutions for the DLP in these semigroups.

Category / Keywords: foundations / discrete logarithm problem, quantum algorithms, semigroups.

Date: received 29 Oct 2013, last revised 2 Nov 2015

Contact author: tsaban at math biu ac il

Available format(s): PDF | BibTeX Citation

Note: To appear in Designs Codes and Cryptography

Version: 20151102:224626 (All versions of this report)

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