An Eecient Non-interactive Statistical Zero-knowledge Proof System for Quasi-safe Prime Products

We present eecient zero-knowledge proof systems for quasi-safe prime products and other related languages. Quasi-safe primes are a relaxation of safe primes, a class of prime numbers useful in many cryptographic applications. Our proof systems achieve higher security and better eeciency than all previously known ones. In particular, all our proof systems are perfect or statistical zero-knowledge, meaning that even a computationally unbounded adversary cannot extract any information from the proofs. Moreover, our proof systems are extremely eecient because they do not use general reductions to NP-complete problems, can be easily parallelized preserving zero-knowledge, and are non-interactive for computationally unbounded provers. The prover can also be eeciently implemented given some trapdoor information and using very little interaction. We demonstrate the applicability of quasi-safe primes by showing how they can be eeectively used in the context of RSA based undeniable signatures to enforce the use of \good" public keys, i.e., keys such that if a signer can convince a recipient of the validity of a signature, then he won't be able to subsequently deny the same signature in case of a dispute.