Cryptological applications of square roots in Zpq

This work describes a challenge-and-response protocol and a protocol for digital signatures, both based on the infeasibility of finding square roots modulo n, a product of two large primes. Both depend on the principle that party A authenticates herself to party B by showing that she is in possession of some secret information, viz. the factorization of n. These protocols differ from most existing protocols in the B only needs very limited computational power, such as can probably be incorporated into a smart card