Metrics on the Sets of Nonsupersingular Elliptic Curves in Simplified Weierstrass Form over Finite Fields of Characteristic Two

• Main Author: Keisuke Hakuta
• Format: Article
• Language: English
• Published: Hindawi Limited 2015-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Online Access: http://dx.doi.org/10.1155/2015/597849

Elliptic curves have a wide variety of applications in computational number theory such as elliptic curve cryptography, pairing based cryptography, primality tests, and integer factorization. Mishra and Gupta (2008) have found an interesting property of the sets of elliptic curves in simplified Weierstrass form (or short Weierstrass form) over prime fields. The property is that one can induce metrics on the sets of elliptic curves in simplified Weierstrass form over prime fields of characteristic greater than three. Later, Vetro (2011) has found some other metrics on the sets of elliptic curves in simplified Weierstrass form over prime fields of characteristic greater than three. However, to our knowledge, no analogous result is known in the characteristic two case. In this paper, we will prove that one can induce metrics on the sets of nonsupersingular elliptic curves in simplified Weierstrass form over finite fields of characteristic two.