Patent ID: 8213605

Claim:
A cryptographic system operating on an elliptic curve E of order n, said cryptographic system comprising a first correspondent for cryptographically processing data for a second correspondent; said first correspondent comprising a memory and a first cryptographic processor, said first cryptographic processor being configured for: storing in said first memory, an endomorphism [z] from one group to another corresponding to a quadratic algebraic integer z that satisfies z 2 +uz+v=0, where u and v are secret integers, and v is relatively prime to n; identifying said endomorphism [z] as a public key operation having a corresponding private key operation [−w]([u]+[z]), where w is an integer, wv=1 mod n, [−w] is an endomorphism corresponding to −w, and [u] is an endomorphism corresponding to u; obtaining data x to be cryptographically processed; applying said public key operation to said data x to obtain modified data x′; and providing said modified data x′ to said second correspondent in said cryptographic system to enable a second cryptographic processor at said second correspondent to perform said private key operation on said modified data x′.