Computability in Europe 2008
Logic and Theory of Algorithms

Regular Talk:
Succinct NP Proofs from an Extractability Assumption

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THIS TALK HAS BEEN CANCELLED!!!
Speaker:	Helger Lipmaa
Author(s):	Giovanni Di Crescenzo and Helger Lipmaa

Abstract

We prove, \emph{using a non-standard complexity assumption}, that any language
in $\NP$ has a \emph{1-round} (that is, the verifier sends a message to the
prover, and the prover sends a message to the verifier) argument system (that
is, a proof system where soundness holds against polynomial-time provers) with
communication complexity \emph{only polylogarithmic in the size of the $\NP$
instance}. We also show formal evidence that the nature of the non-standard
complexity assumption we use is 
analogous to previous assumptions proposed in the cryptographic literature. The
question of whether complexity assumptions of this nature can be considered
acceptable or not remains of independent interest in complexity-theoretic
cryptography as well as complexity theory.