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characteristics three field elliptic curve lliptic curve for characteristics three field

asked 2019-08-02 05:51:15 -0500

santoshi gravatar image

updated 2019-08-03 16:05:56 -0500

slelievre gravatar image

How to generate elliptic curve from the following code as B is in hexadecimal form. The elliptic curve generated from the following code is ... which is not showing B in irreducible polynomial form.

Elliptic Curve defined by $y^2 = x^3 + x^2 + 1$ over Finite Field in $a$ of size $3^{151}$

F1.<x> = GF(3)[]
F.<a> = GF(3^151, 'a', modulus=x^151 + 2*x^2 + 1)
F.modulus()
F
A = 1
A
B = (0x1fc4865afe00a9216b0b5fd32c6300c4bed0707ae4072a03e55299f157b)
B
E = EllipticCurve(F, (0, A, 0, 0, B))
E
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answered 2019-08-02 06:29:26 -0500

rburing gravatar image

The field $F = GF(3^{151})$ is a 151-dimensional vector space over $GF(3)$, so its elements can be viewed as vectors of length 151 with entries in ${0,1,2}$, or as natural numbers $< 3^{151}$ written in base 3. To do the conversion in SageMath, you can do:

B = F(B.digits(3))
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Asked: 2019-08-02 05:51:15 -0500

Seen: 31 times

Last updated: Aug 03 '19