Patent ID: 7231040

Claim:
A processor-implemented method for establishing cryptographic communications, comprising the steps of: encoding a plaintext message word M to a ciphertext word C, wherein M corresponds to a number representative of a message and wherein 0 ≦M≦n− 1, wherein n is a composite number formed by the product of p 1 ·p 2 · . . . ·p k , k is an integer greater than 2 and p 1 , p 2 , . . . p k are distinct random prime numbers, C is a number representative of an encoded form of message word M, and wherein said encoding step comprises transforming said message word M to said ciphertext word C, whereby C≡M e (mod n), and wherein e is a number relatively prime to (p 1 −1), (p 2 −1), . . . , and (p k −1); and decoding said ciphertext word C to a receive message word M′, said decoding step being performed using a decryption exponent d that is defined by d≡e −1 mod ((p 1 −1) (p 2 −1) . . . (p k −1)), said decoding step including the further steps of, defining a plurality of k sub-tasks in accordance with M 1 ′≡C 1 d 1 (mod p 1 ), M 2 ′≡C 2 d 2 (mod p 2 ), . . . M k ′≡C k d k (mod p k ), wherein C 1 ≡C(mod p 1 ), C 2 ≡C(mod p 2 ), . . . C k ≡C(mod p k ), d 1 ≡d(mod(p 1 −1)), d 2 ≡d(mod(p 2 −1)), and . . . d k ≡d(mod(p k −1)), solving said sub-tasks to determine results M 1 ′, M 2 ′, . . . M k ′, and combining said results of said sub-tasks to produce said receive message word M′, wherein M′=M.