# Elliptic Curves and ElGamal [closed]

could you guys please help me with the following problem or tell me where to find an example or something to understand it:

Find a pair of values a and b so that the elliptic curve forms an abelian group module 2459, then find the following: (a) 245 * P where P is an element of the group, specify the value of P (b) 133 * P with the same P from (a) point. (c) Use the Gammal to find the key with the two previous items.

I really appreciate your help. Have a good day.

• Could you further specify the issues you are having solving the problem? – shaun1010 Oct 13 '17 at 20:30
• I'm not pretty sure how to find a and b to make the elliptic curve form an abelian group. – David Oct 13 '17 at 22:25
• I'm voting to close this question as off-topic because it is a homework dump. – fkraiem Oct 14 '17 at 0:31
• While the parts a) and b) are quite uninteresting and c) is unclear due to lack of specification on what is asked for, I have to say that the question that OP is stuck on "Given a curve order $n$ and a finite base-field, find a (weierstrass?) curve that has this order" is quite an intriguing one. I think this question can become a good one, if point c) is clarified by David and preferably a) and b) are researched ("scalar multiplication ecc point"). Even better would be some documentation on possible approaches David has thought of for finding the curve. – SEJPM Oct 14 '17 at 23:18