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• W3100312349 abstract "In quantum cryptography, a one-way permutation is a bounded unitary operator $U:mathcal{H} to mathcal{H}$ on a Hilbert space $mathcal{H}$ that is easy to compute on every input, but hard to invert given the image of a random input. Levin [Probl. Inf. Transm., vol. 39 (1): 92-103 (2003)] has conjectured that the unitary transformation $g(a,x)=(a,f(x)+ax)$, where $f$ is any length-preserving function and $a,x in GF_{{2}^{|x|}}$, is an information-theoretically secure operator within a polynomial factor. Here, we show that Levin's one-way permutation is provably secure because its output values are four maximally entangled two-qubit states, and whose probability of factoring them approaches zero faster than the multiplicative inverse of any positive polynomial $poly(x)$ over the Boolean ring of all subsets of $x$. Our results demonstrate through well-known theorems that existence of classical one-way functions implies existence of a universal quantum one-way permutation that cannot be inverted in subexponential time in the worst ca" @default.
• W3100312349 created "2020-11-23" @default.
• W3100312349 creator A5079497148 @default.
• W3100312349 date "2017-04-27" @default.
• W3100312349 modified "2023-10-16" @default.
• W3100312349 title "Quantum one-way permutation over the finite field of two elements" @default.
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• W3100312349 doi "https://doi.org/10.1007/s11128-017-1599-6" @default.
• W3100312349 hasPublicationYear "2017" @default.
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