An efficient non-interactive statistical zero-knowledge proof system for quasi-safe prime products

We present efficient zer~knowledge proof systems for quasisafe prime products and other related languages. Quasisafe primes are a relaxation of safe primes, a class of prime numbers useti in many cryptographic apphcations. More specifccdy we present the first simple and efficient zer~knowledge proof that an deged RSA modtius is of the correct form, i.e. the product of two primes. N previously known proof enforced ordy that the modtius was the product of two prime powers. We then present a zer~ knowledge proof that the primes composing the RSA moddus are quasi-safe. Our proof systems achieve higher security and better efficiency than ~ previously known ones. In partitiar, W our proof systems are perfect or statisticd zer~knowledge, meaning that even a comput ation~y unbounded adversary cannot extract any information from the proofs. Moreover, our proof systems are extremely efficient because they do not use general reductions to NP-complete problems, can be easfiy pardehzed preserving zer~knowledge, and are noninteractive for comput ationdy unbounded provers. The prover can rdso be efficiently implemented given some trap door information and using very Ettle interaction. We demonstrate the appEcabtity of quasi-safe primes by showing how they can be effectively used in the cent ext of RSA based undeniable signatures to enforce the use of keys of a certain format.