Some ECC Types and Operations

We have a number of possible types of elliptic curve methods. These have a field (the prime number used), the order (the number of elliptic curve points), an a value, a b value, and a generator point (G). For a Weierstrass curve the standard form is y²=x³+ax+b (such as secp256k1). With a twisted Edwards curve (such as Ed25519) we have the form of ax²+y²=1+dx²y². A Montgomery curve has the form of by²=x³+ax²+x.

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Prof Bill Buchanan OBE

Prof Bill Buchanan OBE

Professor of Cryptography. Serial innovator. Believer in fairness, justice & freedom. Based in Edinburgh. Old World Breaker. New World Creator. Building trust.