ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 04 May 2017 23:54:50 +0200I want to compare time of scalar multiplicity between ECC HECC with security level 80https://ask.sagemath.org/question/37514/i-want-to-compare-time-of-scalar-multiplicity-between-ecc-hecc-with-security-level-80/ So in ECC GF(next_prime(2^160)) then construct the curve, base point
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I'm not sure how in hyper elliptic curve;
I think
$ `q = next_prime(2^80)`
$ `K.<x>=GF(q,'x')[]`
$ `f = x^5 + x^3 + 1`
$ `H = HyperellipticCurve(f, 0)`
$ `J = H.jacobian()`
$ `z = Integer(randrange(2, q-2))`
$ `D = J(H.lift_x(F(z)))` # divisor
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To compare time
ECC => `%timeit (Integer(randrange(1, 2^160))) * base point`
HECC => %timeit (Integer(randrange(1, 2^80))) * divisor`
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is this correct?
and if this correct, how ECC time = 13.2 millisecond;
HECC time = 185 millisecondsherifasagewadThu, 04 May 2017 23:54:50 +0200https://ask.sagemath.org/question/37514/change of variable from hyperellictic curve to Weierstrass formhttps://ask.sagemath.org/question/36637/change-of-variable-from-hyperellictic-curve-to-weierstrass-form/ I have the hyperelliptic curve `v^2 = p^4-2*p^3+5*p^2+8*p+4` which I wish to change it to an elliptic curve in Weierstrass form where it returns the change of variable v=[u,r,s,t]. I got the following from Maple. Was wondering if I could get a similar thing using Sage.
-(y^2) = x^3-(121/3)*x-(1690/27)
x = -(1/3)*(5*p^2+24*p-12*v+24)/p^2
y = (-4*p^3 + 20*p^2 + (-8*v + 48)*p + (-16*v + 32))/p^3
p = (-72*x-264+36*y)/(9*x^2+30*x-119)
v = (-162*x^4+540*x^3-648*x^2*y+13176*x^2-4752*x*y+62340*x-16488*y+153994)/(81*x^4+540*x^3-1242*x^2-7140*x+14161)ShaThu, 16 Feb 2017 04:31:48 +0100https://ask.sagemath.org/question/36637/