NPMV-Complete Functions That Compute Discrete Logarithms and Integer Factorization

Hasegawa, Shingo; Isobe, Shuji; Shizuya, Hiroki

doi:10.1093/ietfec/e91-a.1.342

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2013

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“…Note that in [7] they found NPMV-complete functions that directly compute discrete logarithms and integer factorization, where NPMV denotes the class of all partial, multivalued functions computed nondeterministically in polynomial time [15]. Therefore our results should be regarded as a set (or a language) counterpart of the results presented in [7].…”

Section: Introductionmentioning

confidence: 72%

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NP-Complete Sets for Computing Discrete Logarithms and Integer Factorization

Hasegawa

Isobe

Shizuya

2013

IIS

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We explore an NP-complete set such that the problem of breaking a cryptographic scheme reduces to the complete set, where the reduction can be given in a straightforward form like the reduction from the graph isomorphism to the subgraph isomorphism. We construct such NP-complete sets Å DL and Å IF for the discrete logarithm problem modulo a prime and the integer factoring problem, respectively. We also show that the decision version of Diffie-Hellman problem reduces directly to Å DL with respect to the polynomial-time many-one reducibility. These are the first complete sets that have direct reductions from significant cryptographic primitives.

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Section: Introductionmentioning

confidence: 72%

“…Again, the question is, what is such an NP-complete set? This question was posed in [7], but the answer is not known so far.…”

Section: Introductionmentioning

confidence: 99%