3
votes
1answer
54 views

How can I find the order of the group that an elliptic curve is defined over?

I have a Weierstrass elliptic curve (y^2=x^3+a*x+b (mod p) ) How can I find the order of the group itself? I have seen Mathematica has a GroupOrder[] command and WolframAlpha will do it for me, but ...
5
votes
1answer
108 views

Are there groups where the computational Diffie Hellman problem is easy but the discrete log problem is hard?

I know that there are elliptic curve groups, used in pairing-based cryptography, where the decisional Diffie Hellman problem (ie. given $g$, $g^a$, $g^b$ and $c$, determine if $c = g^{ab}$ is easy but ...
2
votes
2answers
120 views

Finite fields in elliptic curve

I have an elliptic curve defined over finite field where $S_1=aP$ . Is it valid to say that $S_1P$ can also be computed. $P$ is the generator of the group. What my real question is that. Should '$a$' ...
1
vote
1answer
153 views

ECC Point Multiplication of Product

I can calculate $Q = a\,b\,G$ in several ways: $Q = a \, (b \, G)$ or $Q = b \, (a \, G)$. These give the same result, as expected. But if I do $c = (a \, b) \bmod n$ where $a \, b$ is much greater ...