1. A method of verifying, by a second party, a digital signature of a first party that was generated using an elliptic curve digital signature algorithm, the method comprising: (a) receiving a public key from the first party, (b) receiving a digital signature from the first party, the digital signature being for an electronic message; (c) identifying domain parameters of an elliptic curve used in elliptic curve cryptography, including identifying a generating point of the elliptic curve; (d) transforming said identified generating point of said (c) into a second generating point as a deterministic function of shared knowledge known to the first party and the second party; and (e) verifying, by the second party, said received digital signature as a function of said received public key, the electronic message, and said identified domain parameters of said (c), in which the second generating point of said (d) is substituted for said identified generating point of said (c), wherein the above steps are performed by at least one computer processor.