Cryptographic method and apparatus for public key exchange with authentication

A method of generating a secure session key between two user devices connected by an insecure communications channel, comprising the following steps performed at both devices:

• transmitting a digitally signed composite quantity to the other device, the composite quantity including a publicly known device identifier IDa and a number Ya derived by a practically irreversible transformation of a secret number Xa that it is unique to the device;
• receiving a similarly structured digitally signed composite quantity from the other device;
• transforming the received digitally signed composite quantity into an unsigned composite quantity containing a device identifier IDb of the other device and a number Yb that was derived by transformation from a secret number Xb that is unique to the other device;
• verifying the identity of the other device from the device identifier IDb;
• and
• generating a session key by performing a practically irreversible transformation involving the numbers Xa and Yb.

A method of authentication in a public key cryptographic system, the method comprising the steps of:

• selecting a unique random number Xi for each cryptographic device to be distributed;
• transforming the number Xi to a new number Yi using a practically irreversible transformation;
• forming a composite quantity by combining the number Yi with a publicly known device identifier IDi;
• digitally signing the composite quantity containing Yi and IDi;
• storing the signed composite quantity and the number Xi permanently in each device;
• exchanging, between two devices, a and b, desiring to establish secured communication, the signed composite quantities stored in each;
• authenticating, in each of the two devices, the identity of the other device;
• and
• generating, in each of the two devices, a session key to be used for secured communication.