Patent Document ID: 8219820
Application ID: 12040212
Patent Flag: 1

Claim One:
1. A non-transitory computer readable medium containing computer-executable instructions that, when performed by a processor given a long-term private cryptographic key and a long-term public cryptographic key, which has been determined based on said long-term private cryptographic key and a base point on a given elliptic curve, said base point having a prime order, cause said processor to: generate a sessional private cryptographic key and a sessional public cryptographic key; determine an implicit signature based on evaluating: 
 S A =[k A +( R A ω)(ω −1 d A )] mod u where S A is said implicit signature; k A is said sessional private cryptographic key; ω is said random number; d A is said long-term cryptographic key; R A is a function of said sessional public cryptographic key, R A ; and u is said order of said base point; determine a shared secret cryptographic key based on said implicit signature; and encrypt a message using said shared secret cryptographic key.