SECURE USER IDENTIFICATION BASED ON RING HOMOMORPHISMS

A method and system is disclosed for performing user identification, digital signatures and other secure communication functions based on ring homomorphisms (220). In one embodiment, a secure user identification technique is disclosed in which one of the system users, referred to as a Prover, randomly selects an element g from the set Rg. The Prover (230) evaluates the homomorphism O(g) (220) to another user referred to as the Verifier. The Verifier randomly selects a challenge element c from the set Rc. The Verifier transmits c to the Prover (230). The Prover (230) generates a response element h using the private key f and the elements c and g. The element h may be generated in the form g*(f+c*g) using addition + and multiplication * in the ring R; or more generally by choosing a set of elements gi, receiving a set of challenge elements ci, creating modified challenge elements dj from the challenge elements ci, transmitting the modified challenge elements di to the Verifier, and generating the response element h as a polynomial function of the secret key f and the selected elements gi, ci, and dj. The Verifier checks that the element h is in the set Rh. The Verifier also evaluates the homomorphism O (220) at the element h and compares the result O(h) to a function of O(g), O(c), and the public key O(f) (240) of the power.