Abstract:
A method of communicating information between users of a communication system includes the following steps of: generating a module V over a ring R; generating an outer component P of encryption key that includes sequence (p, p, . . . , p) where each member pof the sequence belongs to the set {1, 2, . . . , m} (the length k of the sequence is arbitrary and thus repetitions are allowed in the sequence); generating an inner component Q of encryption key that includes elements vv, . . . , Vof V and automorphisms g, g, . . . , gof V; generating the encryption key K=(P; Q), where P is the outer component and Q is the inner component; generating an encryption automorphism Tof V based on the encryption key K, where Tincludes a composition of certain automorphisms T, T, . . . , Tof the module V which composition is performed in the order prescribed by P; generating an encrypted message element E as a function of a message element M in V and of the encryption automorphism T; transmitting the encrypted message element E along with the outer component P from one user to another; generating the outer component P′ of the decryption key that includes sequence (p, p, . . . , p), i.e., the sequence reversed of that involved in producing the outer component P of the encryption key; generating the decryption key K′=(P′; Q′), where P′ is the outer component of the decryption key and Q′ is the inner component of the decryption key which is equal to the inner component Q of the encryption key; generating a decryption automorphism Tof V based on the decryption key K′, where Tincludes a composition of the automorphisms T, T, . . . , T, which composition is performed in the order prescribed by P′, e.g., Tis the inverse automorphism of T; determining the message element M as a function of the encrypted message element E and of the decryption automorphism T, where the function is the same as that one used in generation of E (that is, the decryption method is symmetric to encryption: the decryption proceeds as the encryption, but with replacement of the outer component P with the outer component P′).