Cryptographic communication method and apparatus

A public key cryptographic system including:

• first and second communicating terminals arranged to function respectively as a transmitting and a receiving terminal for electronic signals;
• an encoding device at said first terminal and a decoding device at said second terminal;
• wherein said encoding device has means for encoding a message to be transmitted by transforming the message with an encryption key including encryption numbers e and N to create an encoded message,
• and said decoding device has means for decoding the message by transforming the message with a decryption key using the Lucas functions of the set of numbers D.

In a method of communicating securely over an insecure communication channel of the type which communicates an electronic signal message from a transmitter to a receiver, the improvement which comprises:

• generating a public enciphering key which can be used to encipher messages destined for the receiver, the public enciphering key including two encryption numbers e and N;
• generating a secret deciphering key including a set of numbers D for use at the receiver,
• by computing the set of numbers D from e and the prime factors of N;
• processing the message at the transmitter by:
• digitizing said message;
• separating said digitized message into sections each comprising a number less than N;
• computing a cryptogram section corresponding to each section of the digitized message, using the Lucas function of e to create an enciphered message containing the cryptogram sections;
• transmitting the enciphered message;
• and processing the enciphered message at the receiver to decode each cryptogram section by transforming them with the Lucas functions of the set of numbers D.

A method of providing a digital signature for a communicated electronic signal message comprising the steps of:

• providing a public verification key, including two verification numbers e and N;
• generating a secret signing key including a set of numbers D wherein the numbers of the set D are derived from e and the prime factors of N such that the secret signing key is directly related to and computationally infeasible to generate from the public verification key;
• processing the message to be transmitted and the secret signing key at the transmitter to generate a digital signature at said transmitter by transforming a representation of the message with the secret signing key, by calculating the Lucas function of the set of numbers D such that the digital signature is computationally infeasible to generate from the public verification key;
• communicating the public verification key to the receiver;
• transmitting the message and the digital signature from the transmitter to the receiver;
• receiving the message and the digital signature at the receiver and transforming said digital signature with the public verification key by calculating the Lucas function of e to generate a representation of the message;
• and
• validating the digital signature by comparing the similarity of the message to the representation of the message generated from the digital signature.