| 摘要 |
A method of verifying the authenticity of a message transmitted from a sender to a receiver in a communication system is partitioned into three stages. In the first stage, a key is secretly exchanged between the sender and receiver. This key is a binary irreducible polynomial p(x) of degree n. In addition, the sender and receiver share an encryption key composed of a stream of secret random, or pseudo-random bits. In the second stage, the sender appends a leading non-zero string of bits, which, in the simplest case, may be a single "1" bit, and n tail bits "0" to M to generate an augmented message, this augmented message considered as a polynomial having coefficients corresponding to the message bits. If the length of the message is known and cryptographically verified, then there is no need for a leading "1". The sender then computes a polynomial residue resulting from the division of the augmented message polynomial generated by the key polynomial p(x) exchanged by the sender and receiver. The sender encrypts the computed residue. Preferably, the encryption is done by performing a bitwise Exclusive OR operation between the bits of the residue and the stream of secret bits shared by the sender and receiver. The sender then transmits the message M and the encrypted residue. The third stage is performed by the receiver by decrypting the transmitted encrypted residue at the time of reception. The receiver then appends the decrypted residue to the end of the received message M to obtain a combined bit stream M'. The receiver computes the residue of the division between the binary polynomial represented by the bit stream M' and the key polynomial p(x) exchanged by the sender and receiver. The receiver accepts a received message M as authentic only if the residue computed is zero.
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