I implemented the algorithm published in ECC Brainpool to generate
random elliptic curves.
http://tools.ietf.org/html/draft-lochter-pkix-brainpool-ecc-02#page-21
Need to calculate an optimal way to solve in sage de point 4 and 8 of
the algorithm
The following procedure is used to generate the parameters A and B
of
a suitable elliptic curve over GF(p) and a base point G from a
prime
p of bit length L and a 160 bit seed s.
1. Set A = find_integer_2(s).
2. Convert h to an integer A.
3. If - 3 = A* Z^4 is not solvable, then set s = update_seed(s)
and
goto Step 1.
4. Compute one solution Z of - 3 = A* Z^4.
5. Set s = update_seed(s).
6. Set B = find_integer_2(s).
7. If B is a square mod p, then set s = update_seed(s) and goto
step 6.
8. If 4*A^3 + 27*B^2 = 0, then set s = update_seed(s) and goto
Step
1.
Thanks.
--
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to
sage-support+unsubscr...@googlegroups.com
For more options, visit this group at
http://groups.google.com/group/sage-support
URL: http://www.sagemath.org
