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arXiv · 1306.1447

Semigroups and one-way functions

J. C. Birget
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Abstract

We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. Then P is not equal to NP iff fP is a non-regular semigroup. The one-way functions considered here are based on worst-case complexity (they are not cryptographic); they are the non-regular elements of fP. We prove various properties of fP, e.g., that it is finitely generated. We define reductions with respect to which certain universal one-way functions are fP-complete.

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J. C. Birget. 2015-03-06. Semigroups and one-way functions. https://doi.org/10.1142/s0218196715400019

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