Elliptic Curves Cryptography
Independent thesis Advanced level (degree of Master (Two Years)), 15 credits / 22,5 HE creditsStudent thesis
In the thesis we study the elliptic curves and its use in cryptography. Elliptic curvesencompasses a vast area of mathematics. Elliptic curves have basics in group theory andnumber theory. The points on elliptic curve forms a group under the operation of addition.We study the structure of this group. We describe Hasse’s theorem to estimate the numberof points on the curve. We also discuss that the elliptic curve group may or may not becyclic over finite fields. Elliptic curves have applications in cryptography, we describe theapplication of elliptic curves for discrete logarithm problem and ElGamal cryptosystem.
Place, publisher, year, edition, pages
2012. , 42 p.
Group Theory and Number Theory; Elliptic Curves; Elliptic Curves over Finite Fields; Applications of Elliptic Curves.
IdentifiersURN: urn:nbn:se:lnu:diva-17552OAI: oai:DiVA.org:lnu-17552DiVA: diva2:502112
Subject / course
Mathematics and Modelling, Master Programme, 120 credits
2012-02-07, B2034, Linnéuniversitetet, Linnaeus University, Växjö, 14:00 (English)
UppsokPhysics, Chemistry, Mathematics
Svensson, Per Anders