| 摘要 |
<p>A public key cryptographic system uses Lucas functions as the basis for encoding and decoding messages. An encoding device and a decoding device are linked by a communication channel. The first device is able to be actuated by some message to be transmitted, M, as well as an encryption key, E, so as to form a cryptogram, C, so that C can be sent over the communication channel to a decoding device. The encryption key, E, is a pair of positive whole numbers, e and N, which match the decryption key, D, of the second decoding device. The message M must usually be broken down into blocks, Mi, such that each is greater than or equal to zero and less than or equal to N - 1. N is a composite number - i.e. it is made up of at least two prime numbers, p and q, such that N = p.q. The cryptographic transformation done by the encoding device can be described using the notation of Lucas functions. It is, for each ith block of message M which produces a matching ith block of the cryptogram C: Ci = Ve (Mi, 1) (modulo N) where e hasbeen chosen to be relatively prime to all of (p-1), (q-1), (p+1) and (q+1).</p> |
