Applications of Elliptic Curves in Cryptography

Author(s): 

Marisol Espinoza, Undergraduate

Advisor(s):

Ivona Grzegorczyk, Mathematics

Discipline:

Mathematics

Abstract:

Cryptography is the area of study that uses algorithms to encrypt and decrypt data; using public or private key cryptography. Elliptic curves have been studied ever since the third century A.C., but recently elliptic curve cryptography as encryption scheme for public-key encryption has gained traction due to its ability to generate a higher level of security while requiring a drastically reduced amount of computational power. This scheme is based on Lenstra’s elliptic-curve factorization and the chord-and-tangent method and can be proven using Fermat’s little theorem. We consider a specific elliptic curve to explain how to send an encrypted message (a number) via elliptic curve cryptography (ECC) and then decode it.

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