10-06-2017, 07:05 AM
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This project studies the mathematics of elliptic curves, starting with their
derivation and the proof of how points upon them form an additive abelian
group. We then work on the mathematics neccessary to use these groups
for cryptographic purposes, specifically results for the group formed by an
elliptic curve over a finite field, E(Fq). We examine the mathematics behind
the group of torsion points, to which every point in E(Fq) belongs, and
prove Hasse s theorem along with a number of other useful results. We finish
by describing how to define a discrete logarithm problem using E(Fq) and
showing how this can form public key cryptographic systems for use in both
encryption and key exchange.