A reduction of Semigroup DLP to classic DLP

Matan Banin, Boaz Tsaban

Research output: Contribution to journalArticlepeer-review


We present a polynomial-time reduction of the discrete logarithm problem (DLP) in any periodic (or torsion) semigroup (Semigroup DLP) to the classic DLP in a subgroup of the same semigroup. It follows that Semigroup DLP can be solved in polynomial time by quantum computers, and that Semigroup DLP 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.

Original languageEnglish
Pages (from-to)75-82
Number of pages8
JournalDesigns, Codes, and Cryptography
Issue number1
StatePublished - 1 Oct 2016


  • Discrete logarithm problem
  • Quantum algorithms
  • Semigroups

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Applied Mathematics


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