Ring-based public key cryptosystem method

摘要

A method of communicating information between users of a communications system includes the following steps: generating a ring R, ideals P and Q in R, a set of coset representatives C_Q for the ring R modulo the ideal Q, and a set of coset representatives C_p for the ring R modulo the ideal P; generating at least one public key element h₁, . . . , h_k in the ring R as a function of at least two private key elements ƒ₁, . . . ƒ_n in R and the ideal Q of the first user; and transmitting from a first user to a second user a description of the ring R, the ideal Q, the ideal P, and the elements h₁, . . . , h_k in R; generating an element e in R as a function of the ideals P and Q, the public key elements h₁, . . . , h_k, a private message element m in R, and at least one private random element ø₁, . . . , ø_l of the second user; and transmitting the element e from the second user to the first user, such that the first user can determine the message element m by computing a result A in R of evaluating a function F of e, ƒ₁, . . . , ƒ_n, computing a coset representative a of A in the set of coset representatives C_q, computing a result B of evaluating a function G of a, ƒ₁, . . . , ƒ_n, computing a coset representative b of B in the set of coset representatives C_p, and computing a result c in the set of coset representatives C_p of evaluating a function H of b, ƒ₁, . . . , ƒ_n.