Patent ID: 8462939

Claim:
A Residue Number System (RNS)-based cryptographic method for encrypted communications over a communications channel using a cryptographic device, comprising the steps of: embedding data strings corresponding to a plaintext message into a set of message integers, the message integers being residues of corresponding elements of a basis of the residue number system having elements relatively prime pairwise to each other, the basis being previously agreed upon and kept secret; forming a set of cipher elements by raising each of the message integers to a first non-zero integer power, multiplying by a selected integer raised to a second power, and taking the result modulo the corresponding element of the basis, the first and second powers being previously agreed upon and kept secret; combining the set of cipher elements to form a cipher integer vector; converting the cipher integer vector into a cipher integer value using corresponding elements of the basis and the Chinese Remainder Theorem; sending the cipher integer value to a receiving correspondent; upon receipt of the message encrypted into a cipher integer value, converting the received cipher integer value to a set of cipher elements by determining the residues of the received cipher integer value modulo the corresponding elements of the basis; converting the cipher elements of the received message to the corresponding message integers using a corresponding correlate of the agreed upon secret first power, secret second power, and the inverse of the selected integer modulo the corresponding element of the basis; and recovering the plaintext message from the message integers.