Quantum computation of discrete logarithms in semigroups

@article{Childs2014QuantumCO,
title={Quantum computation of discrete logarithms in semigroups},
author={Andrew M. Childs and G. Ivanyos},
journal={Journal of Mathematical Cryptology},
year={2014},
volume={8},
pages={405 - 416}
}
• Published 2014
• Computer Science, Mathematics, Physics
• Journal of Mathematical Cryptology
• Abstract We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and the discrete logarithm problem as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete logarithms in semigroups are insecure against quantum attacks. In contrast, we show that some generalizations of the discrete logarithm problem are hard in semigroups despite being easy in groups. We relate a shifted version of the… CONTINUE READING
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References

SHOWING 1-10 OF 29 REFERENCES
Quantum algorithm for discrete logarithm problem for matrices over finite group rings
• Computer Science, Mathematics
• Groups Complex. Cryptol.
• 2012
• 13
• PDF
Public key cryptography based on semigroup actions
• Computer Science, Mathematics
• 2007
• 60
• Highly Influential
• PDF
Hidden Translation and Translating Coset in Quantum Computing
• Mathematics, Computer Science
• SIAM J. Comput.
• 2014
• 15
• PDF
On Quantum Algorithms for Noncommutative Hidden Subgroups
• Mathematics, Computer Science