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• W2068363706 abstract "We show that there is a pair of disjoint N P -sets, whose disjointness is provable in S 1 2 and which cannot be separated by a set in P /poly, if the cryptosystem RSA is secure. Further we show that factoring and the discrete logarithm are implicitly definable in any extension of S 1 2 admitting an N P -definition of primes about which it can prove that no number satisfying the definition is composite. As a corollary we obtain that the Extended Frege (EF) proof system does not admit a feasible interpolation theorem unless the RSA cryptosystem is not secure and that an extension of EF by tautologies τ p ( p primes), formalizing that p is not composite, as additional axioms do not admit a feasible interpolation theorem unless factoring and the discrete logarithm are in P /poly." @default.
• W2068363706 created "2016-06-24" @default.
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• W2068363706 creator A5069803587 @default.
• W2068363706 date "1998-01-01" @default.
• W2068363706 modified "2023-09-25" @default.
• W2068363706 title "Some Consequences of Cryptographical Conjectures forS12and EF" @default.
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• W2068363706 doi "https://doi.org/10.1006/inco.1997.2674" @default.
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