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All reports by Author Konstantin Pervyshev:

TR06-131 | 6th October 2006
Konstantin Pervyshev

On Heuristic Time Hierarchies

We study the existence of time hierarchies for heuristic (average-case) algorithms. We prove that a time hierarchy exists for heuristics algorithms in such syntactic classes as NP and co-NP, and also in semantic classes AM and MA. Earlier, Fortnow and Santhanam (FOCS'04) proved the existence of a time hierarchy for ... more >>>

TR06-046 | 1st April 2006
Dima Grigoriev, Edward Hirsch, Konstantin Pervyshev

A Complete Public-Key Cryptosystem

Comments: 1

We present a cryptosystem which is complete for the class of probabilistic public-key cryptosystems with bounded error. Besides traditional encryption schemes such as RSA and El Gamal, this class contains probabilistic encryption of Goldwasser-Micali as well as Ajtai-Dwork and NTRU cryptosystems. The latter two are known to make errors with ... more >>>

TR05-111 | 3rd October 2005
Dieter van Melkebeek, Konstantin Pervyshev

A Generic Time Hierarchy for Semantic Models With One Bit of Advice

We show that for any reasonable semantic model of computation and for
any positive integer $a$ and rationals $1 \leq c < d$, there exists a language
computable in time $n^d$ with $a$ bits of advice but not in time $n^c$
with $a$ bits of advice. A semantic ... more >>>

TR05-076 | 2nd July 2005
Dima Grigoriev, Edward Hirsch, Konstantin Pervyshev

Time hierarchies for cryptographic function inversion with advice

We prove a time hierarchy theorem for inverting functions
computable in polynomial time with one bit of advice.
In particular, we prove that if there is a strongly
one-way function, then for any k and for any polynomial p,
there is a function f computable in linear time
with one ... more >>>

TR05-054 | 19th May 2005
Konstantin Pervyshev

Time Hierarchies for Computations with a Bit of Advice

A polynomial time hierarchy for ZPTime with one bit of advice is proved. That is for any constants a and b such that 1 < a < b, ZPTime[n^a]/1 \subsetneq ZPTime[n^b]/1.

The technique introduced in this paper is very general and gives the same hierarchy for NTime \cap coNTime, UTime, ... more >>>

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