Quantum algorithm for the discrete logarithm problem for matrices over finite group rings

A.  D.  Myasnikov; A.  Ushakov

Paper 2012/574

Quantum algorithm for the discrete logarithm problem for matrices over finite group rings

A. D. Myasnikov and A. Ushakov

Abstract

We propose a polynomial time quantum algorithm for solving the discrete logarithm problem in matrices over finite group rings. The hardness of this problem was recently employed in the design of a key-exchange protocol proposed by D. Kahrobaei, C. Koupparis, and V. Shpilrain. Our result implies that the Kahrobaei et al. protocol does not belong to the realm of post-quantum cryptography.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Not yet submitted
Keywords: Group-based cryptography semidirect product matrix monoids group-rings Diffie-Hellman key-exchange discrete logarithm problem quantum algorithms post-quantum cryptography
Contact author(s): amyasnik @ stevens edu
History: 2012-10-14: received
Short URL: https://ia.cr/2012/574
License: CC BY

BibTeX

@misc{cryptoeprint:2012/574,
      author = {A.  D.  Myasnikov and A.  Ushakov},
      title = {Quantum algorithm for the discrete logarithm problem for matrices over finite group rings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/574},
      year = {2012},
      url = {https://eprint.iacr.org/2012/574}
}