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Quantum one-way permutation over the finite field of two elements | | Alexandre de Castro
; | | Date: |
5 Sep 2016 | | Abstract: | In quantum cryptography, a quantum one-way permutation is a one-to-one and
onto, (secure) unitary mapping that is easy to compute on every input, but hard
to invert given the image of a random input. Levin(2003) has conjectured that
the mapping 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 permutation
within a polynomial factor.Here, we prove that Levin one-way permutation is a
secure unitary operator because the probability of inverting it approaches zero
faster than the reciprocal of any positive polynomial p(x) over the Boolean
ring of all subsets of x. Our result demonstrates by well-known theorems that
existence of one-way functions implies existence of a quantum one-way
permutation. | | Source: | arXiv, 1609.1541 | | Services: | Forum | Review | PDF | Favorites | |
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