Complexity Measures For Public-Key Cryptosystems

Grollmann, Joachim; Selman, Alan L.

doi:10.1109/sfcs.1984.715952

Cited by 42 publications

(50 citation statements)

References 17 publications

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“…Berman (1977) showed via a relativizable proof that the complete ≤ p m -degree for EXP collapses to a 1-li-degree (one-to-one length-increasing mreductions). By results in Grollmann & Selman (1988) and Ko et al (1987), all 1-li-degrees collapse if and only if P = UP, again by a relativizable proof. Relative to A we have P = UP and P NP = EXP.…”

Section: Phase 2 Codingmentioning

confidence: 74%

Two oracles that force a big crunch

Buhrman

Fenner

Fortnow

et al. 2001

Computational Complexity

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We construct an oracle A such that NEXP A = P NP A . The construction of this oracle answers a long standing open question first posed by Heller, and unsuccessfully attacked many times since. For the first construction of the oracle, we present a new type of injury argument that we call "resource-bounded injury." In the special case of the construction of this oracle, a tree method can be used to transform unbounded search into exponentially bounded, hence recursive, search. This transformation of the construction can be interleaved with another construction so that relative to the new combined oracle also P = UP = NP ∩ coNP. This leads to the curious situation where LOW(NP) = P, but LOW(P NP ) = NEXP, and the complete ≤ p m -degree for P NP collapses to a single p-isomorphism type.

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Section: Phase 2 Codingmentioning

confidence: 74%

Two oracles that force a big crunch

Buhrman

Fenner

Fortnow

et al. 2001

Computational Complexity

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“…By definition UP is a subset of NP. A classical result tells that UP equals P if and only if one-way functions do not exist (see [14]). The primality problem is a typical example of a problem in UP not known to be in P (see [12]).…”

Section: Some Rice-style Theorems For Counting Problemsmentioning

confidence: 99%

Looking for an Analogue of Rice's Theorem in Circuit Complexity Theory

Borchert

Stephan

2000

MLQ - Math. Log. Quart.

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“…It is relatively easy to show that (P1) implies the rest and that (P4) and (P5) each imply (P3). Grollmann & Selman (1988) showed that (P4) also implies (P2). Can we demonstrate any other relationships consistent with these?…”

Section: Introductionmentioning

confidence: 95%

“…They also constructed an oracle B such that P B = UP B = NP B ∩ coNP B . Grollmann & Selman (1988) showed that P = UP iff one-way functions do not exist and that all disjoint pairs of NP are P-separable iff weak one-way functions do not exist. Thus, because the negation of (P3) implies the negation of (P4), relative to B there are weak one-way functions but no one-way functions.…”

Section: Introductionmentioning

confidence: 99%