A Comparison of Random Elliptic Curves and Finite Fields Suitable for Cryptography

M.S.H. Kuroda and D.C.C. Bover (USA)

Keywords

Cryptography , Elliptic Curve, Finite Field

Abstract

Cryptography is becoming more and more important in today's world as secure communication is expanded through online transactions. A secure form of communication between two people that have never meet can be established through public-key encryption. One of the newest, and considered most secure, forms of public key encryption uses elliptic curves. Among the strengths of a cryptosystem based on elliptic curves is the multiple ways to create the elliptic curve and its underlying finite field without losing security. This paper looks at three basic implementations for an elliptic curve's underlying field; the general prime field and characteristic two extension fields using a polynomial basis and an optimal normal basis, and compares the performance of the calculated algorithms for these forms.

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