sage: var('x,y')
(x, y)
sage: E = EllipticCurve(y^2 == x^3 - 36*x)
sage: P=E(-3,9)
sage: Q=E(12,36)
sage: discrete_log(Q, P, operation='+', bounds=(0,100))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
...
ValueError: No discrete log of (12 : 36 : 1) found to base (-3 : 9 : 1)
There is no such n, despite P being a generator. Maybe there's some torsion?
sage: E.torsion_order()
4
sage: discrete_log(4*Q, P, operation='+', bounds=(0,100))
4
sage: (P - Q)
(0 : 0 : 1)
sage: (P - Q).height()
0
sage: discrete_log??
Totally generic discrete log function.
INPUT:
- ``a`` - group element
- ``base`` - group element (the base)
- ``ord`` - integer (multiple of order of base, or ``None``)
- ``bounds`` - a priori bounds on the log
- ``operation`` - string: '*', '+', 'other'
- ``identity`` - the group's identity
- ``inverse()`` - function of 1 argument ``x`` returning inverse of ``x``
- ``op()`` - function of 2 arguments ``x``, ``y`` returning ``x*y`` in group
...
On Sat, May 26, 2012 at 2:14 PM, raman kurdi <[email protected]> wrote:
> Hi Dears,
> I have the elliptic curve Y^2=X^3-36X and P=(-3,9) as the its
> generator. Q=(12,36) is the other point on this curve. I would like to
> solve Discrete Logarithm but I do not know.
> Please tell me how I can find the "n" which nQ=p.
> Best,
> Raman
>
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