a long term private key d of the correspondent 12 in an elliptic curve cryptosystem ecc with know parameters including a generating point p of order n the correspondent 12 randomly generates a ephemeral private key k and computes a corresponding ephemeral public kp which represents a point with coordinates x y to compute a first component r of the signature the first co ordinate of the ephemeral public key kp is converted into an integer the first component is itself random as it is determined from the random private key k a second component s of the signature is generated by solving the signing equation ks h i dr mod n for the second component s of the signature where h is an appropriate cryptographic hash function such as sha1 the information and signature is assembled as a data stream 26 containing i r s in defined locations and is then transmitted as the signed message 28 through the link 16 upon reception of the signed message 28 at the correspondent 14 the cryptographic processor 20 proceeds to authenticate the signature the authentication normally proceeds as follows initially the ephemeral public key kp is computed by calculating s u2212 1 h i p ra where a is the long term public key of the correspondent 12 after recovery of kp the first co ordinate of kp is converted into an integer following the same procedure as used by the correspondent 12 the integer obtained should correspond to the number r contained in the transmission and if so the signature is accepted if it does not the signature is not verified and so is rejected to inhibit a replay attack a subject f r of the number r is.