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.Sat, 06 Jan 2018 21:49:39 +0100Set a specific polynomial as a divisor of hyper elliptic curvehttps://ask.sagemath.org/question/40509/set-a-specific-polynomial-as-a-divisor-of-hyper-elliptic-curve/ If I have a hyperelliptic curve of genus 2 = y2+( x2+x)y = x5+ x3 +1
and reduced divisor for the curve in Mumford is (x2+18x, 17x+1).
the two was given, I can construct the curve: as k.<a> = GF(next_prime(2^160)); R.<x> = k[]
C = HyperellipticCurve(x^5 + x^3 + 1, x^2+x)
How to set (x2+18x, 17x+1) as it's divisor
sherifasagewadSat, 06 Jan 2018 21:49:39 +0100https://ask.sagemath.org/question/40509/I 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/