Stream cipher based on quasigroup string transformations in Zp*

In this paper we design a stream cipher that uses the algebraic structure of the multiplicative group Z Z * p (where p is a big prime number used in ElGamal algorithm), by defining a quasigroup of order p − 1 and by doing quasigroup string transformations. The cryptograph-ical strength of the proposed stream cipher is based on the fact that breaking it would be at least as hard as solving systems of multivari-ate polynomial equations modulo big prime number p which is NP-hard problem and there are no known fast randomized or deterministic algorithms for solving it. Unlikely the speed of known ciphers that work in Z Z * p for big prime numbers p, the speed of this stream cipher both in en-cryption and decryption phase is comparable with the fastest symmetric-key stream ciphers.