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)
Short URL: ia.cr/2013/707
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