| 摘要 |
A method is disclosed whereby two parties can establish a cryptographic key for secure communications without any prior distribution of secret keys or other secret data, and without revealing said key to any third party who may have access to all of the transmissions between them. The two parties agree upon a matrix M, and independently choose matrices S and R from an established commutative family of square matrices. The sender transmits the matrix SM to the receiver and the receiver transmits the matrix RM to the sender. The sender computes the matrix SRM from the received matrix RM, and the receiver computes the matrix RSM from the received matrix SM. Since the matrices S and R commute, SRM=RSM. The value of the matrix SRM is then used to produce the desired cryptographic key. In the two-sided embodiments the two parties agree upon a matrix M, and two commutative families of square matrices F and G. The sender chooses a matrix S from F and a matrix T from G. The receiver independently chooses a matrix R from F and a matrix Q from G. The sender transmits the matrix SMT to the receiver and the receiver transmits the matrix RMQ to the sender. The sender computes the matrix SRMQT from the received matrix RMQ, and the receiver computes the matrix RSMTQ from the received matrix SMT. Since the matrices S and R commute, and the matrices T and Q commute, SRMQT=RSMTQ. The value of the matrix SRMTQ is then used to produce the desired cryptographic key. |
