Level: MSci, MSc
Title: Elliptic curve cryptography
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Research Area: Algebra
Description:

An elliptic curve is a cubic curve of the form y2  =  ax3 + bx2 + cx + d. It can be made into an abelian group in such a way that three points sum to zero if and only if they lie on a straight line. (The associative law is quite tricky to prove!) It is possible to design a public-key cryptosystem analogous to RSA, using elliptic curves over finite fields in place of modular arithmetic. Find out about this and explain it in your own words.

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