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Edwards curves and CM curves
Edwards curves are a particular form of elliptic curves that admit a fast,
unified and complete addition law. Relations between Edwards curves and
Montgomery curves have already been described. Our work takes the view of
parameterizing elliptic curves given by their j-invariant, a problematic that
arises from using curves with complex multiplication, for instance. We add to
the catalogue the links with Kubert parameterizations of X0(2) and X0(4). We
classify CM curves that admit an Edwards or Montgomery form over a finite
field, and justify the use of isogenous curves when needed
Elliptic Curves
Elliptic curves have found widespread use in number theory and applications thereof, such as cryptography. In this paper we will first examine the basic theory of elliptic curves and then look specifically at how they can be used to construct cryptographic systems more efficient than their counterparts, and how they can be used to generate proofs for or against primality
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