2020 IB Extended Essays

Elliptic curves play a critical role in number theory, and those over finite fields can be applied for integer factorization and to cryptography. The central principle in most such applications is the rewriting of an algorithm that uses certain finite groups to use, instead, the groups of elliptic curves’ rational points. Based on the algebraic structure of such elliptic curves over finite fields, elliptic-curve cryptography provides an approach to apply to public- key cryptography, digital signatures, encryption, key agreement, pseudo-random generators, etc. Similarly, elliptic curves such as the Lenstra elliptic-curve factorization that have applications in cryptography are utilized in several integer factorization algorithms ( Elliptic- curve cryptography , Wikipedia).

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