An Efficient Identification Scheme Based on Permuted Kernels (Extended Abstract)

In 1985 Goldwasser Micali and Rackoff proposed a new type of interactive proof system which reveals no knowledge whatsoever about the assertion except its validity. The practical significance of these proofs was demonstrated in 1986 by Fiat and Shamir, who showed how to use efficient zero knowledge proofs of quadratic residuosity to establish user identities and to digitally sign messages. In this paper we propose a new zero knowledge identification scheme, which is even faster than the Fiat-Shamir scheme, using a small number of communicated bits, simple 8-bit arithmetic operations, and compact public and private keys. The security of the new scheme depends on an NP-complete algebraic problem rather than on factoring, and thus it widens the basis of public key cryptography, which has become dangerously dependent on the difficulty of a single problem.