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