# realistic Elliptic curve

asked 2017-06-06 05:38:34 -0500 This post is a wiki. Anyone with karma >750 is welcome to improve it.

I have implemented algorithm by considering new approach for elliptic curve arithmetic.(point addition and point doubling) algorithm 1 based on prime field (p=5,13,751,1277) i can't test more than 5 digit.

algorithm 2 based on extension field(2^3,2^4,2^5,2^8)

i want to verify mt results on realistic elliptic curve which is used for application purpose .

please suggest the curve.

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A realistic example would have a prime like $p=2^{200}+235$, next prime after that $2$-power.

sage: (2^200).next_prime()-2^200
235


So a possible start would be:

sage: p = (2^200).next_prime()
sage: E = EllipticCurve( GF(p), [1,2017] )
sage: A = E.random_point()
sage: A
(284049281751646938801730319645266853673910787725918741455027 : 1116776355053931224281164180196737086851307515529089701180450 : 1)
sage: B = E.random_point()
sage: B
(410304091068744772318672322841886177894934951840154004893742 : 636491166324735676220545942927560139611460884479724079090032 : 1)
sage: A+B
(248247578114491954668733481192702435880120988159659889366794 : 831979770562241852274968540703631804748484642250853925692569 : 1)