Ask Your Question

Revision history [back]

click to hide/show revision 1
initial version

implement given divisor as a specific hyperelliptic curve divisor

I get the values from a research paper to ensure (u, v) are correct

A Secured Cloud System using Hyper Elliptic Curve and in sage: p = 4112543547855339322343814790708185367671872426434747235319998473455582535888229747778325047393413053

K = GF(p)

R.<x> = K[]

f = x^5 + 7943193x^4 + 6521255x^3 + 1065528x^2 + 3279922x + 3728927

C = HyperellipticCurve( f )

J = C.jacobian()

X = J(K)

u, v = x^2 + 22457213658579645161x + 62960708771725664757, 65279057408798633572x + 32004384923913711271

D = X( [u,v] )

"error"

implement given divisor as a specific hyperelliptic curve divisor

I get the values from a research paper to ensure (u, v) are correct

A Secured Cloud System using Hyper Elliptic Curve and in sage: p = 4112543547855339322343814790708185367671872426434747235319998473455582535888229747778325047393413053sage:

p = 4112543547855339322343814790708185367671872426434747235319998473455582535888229747778325047393413053

K = GF(p)

GF(p)

R.<x> = K[]

K[]

f = x^5 + 7943193x^4 7943193*x^4 + 6521255x^3 6521255*x^3 + 1065528x^2 1065528*x^2 + 3279922x 3279922*x + 3728927

3728927

C = HyperellipticCurve( f )

)

J = C.jacobian()

C.jacobian()

X = J(K)

J(K)

u, v = x^2 + 22457213658579645161x 22457213658579645161*x + 62960708771725664757, 65279057408798633572x 65279057408798633572*x + 32004384923913711271

32004384923913711271

D = X( [u,v] )

)

"error"

implement given divisor as a specific hyperelliptic curve divisor

I get the values of a divisor for a hyperelliptic curve from a research paper to ensure (u, v) are the divisor is correct and i want to use this divisor on calculation.

so Idid the following:

A Secured Cloud System using Hyper Elliptic Curve and in sage:

p = 4112543547855339322343814790708185367671872426434747235319998473455582535888229747778325047393413053
 K = GF(p)
 R.<x> = K[]

f = x^5 + 7943193*x^4 + 6521255*x^3 + 1065528*x^2 + 3279922*x + 3728927
 C = HyperellipticCurve( f )
 J = C.jacobian()
 X = J(K)

u, v = x^2 + 22457213658579645161*x + 62960708771725664757, 65279057408798633572*x + 32004384923913711271
 D = X( [u,v] )

"error"

verbose 0 (3324: multi_polynomial_ideal.py, groebner_basis) Warning: falling back to very slow toy implementation. verbose 0 (1083: multi_polynomial_ideal.py, dimension) Warning: falling back to very slow toy implementation. Error in lines 9-9 Traceback (most recent call last):
File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1013, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "/ext/sage/sage-8.1/local/lib/python2.7/site-packages/sage/schemes/hyperelliptic_curves/jacobian_homset.py", line 145, in __call__ return JacobianMorphism_divisor_class_field(self, tuple(P)) File "/ext/sage/sage-8.1/local/lib/python2.7/site-packages/sage/schemes/hyperelliptic_curves/jacobian_morphism.py", line 388, in __init__ polys, C)) ValueError: Argument polys (= (x^2 + 22457213658579645161x + 62960708771725664757, 65279057408798633572x + 32004384923913711271)) must be divisor on curve Hyperelliptic Curve over Finite Field of size 4112543547855339322343814790708185367671872426434747235319998473455582535888229747778325047393413053 defined by y^2 = x^5 + 7943193x^4 + 6521255x^3 + 1065528x^2 + 3279922x + 3728927.

Does this mean the paper is wrong or I am at wrong. and if so, how can I modify my work?