Key Agreement and Transport Protocol with Implicit Signatures

Abstract

A key establishment protocol between a pair of correspondents includes the generation by each correspondent of respective signatures. The signatures are derived from information that is private to the correspondent and information that is public. After exchange of signatures, the integrity of exchange messages can be verified by extracting the public information contained in the signature and comparing it with information used to generate the signature. A common session key may then be generated from the public and private information of respective ones of the correspondents.

1 . A system to authenticate a pair of correspondents A, B to permit exchange of information therebetween over a data communication channel, said correspondents having a respective private key a, b and a public key pA, pB derived from a generator α and respective ones of said private keys a, b, said system including a cryptographic unit at each of said correspondents, said cryptographic unit at a first of said correspondents A i) selecting a first random integer x and exponentiating a function f(α) including said generator to a power g(x) to provide a first exponentiated function f(α) g(x) ; (ii) said cryptographic processor of said first correspondent A generating a first signature s A  from said first random integer x and said exponentiated function function f(α) g(x) ; (iii) said cryptographic unit of said first correspondent A forwarding to a second correspondent B a message including said first exponentiated function f(α) g(x)  and said signature s A ; (iv) said cryptographic unit at said second correspondent B selecting a second random integer y and exponentiating a function f(α) including said generator to a power g(y) to provide a second exponentiated function f(α) g(y)  and generating a signature s B  obtained from said second integer y and said second exponentiated function f(α) g(y) ; (v) said cryptographic unit of said second correspondent B forwarding a message to said first correspondent A including said second exponential function f(α) g(y)  and said signature s B ; (vi) each of cryptographic units at said correspondents verifying the integrity of messages received by them by computing from said signature and said exponentiated function in such a received message a value equivalent to said exponentiated function and comparing said computed value and said transmitted value; (vii) each of said cryptographic units of said correspondents constructing a session key K by exponentiating information made public by another of said correspondents with said first random integer that is private to itself.