# Tag Info

3

I'm not sure if I get your question correctly. Do you like to use a 256 bit curve to generate a (secret) key of this size and later drop 192 bits? If this is the case your 64 bits will be useless because you secret key will not have any relation with the public. Furthermore, in a magic case that this works, your field operations will continue living in a 256 ...

2

As mentioned by Thekwasti, what you want here is compute a discrete logarithm, but while it is true that in general computing discrete logarithms is "hard" (which is why they are used in cryptography), in your case the group is small enough to make even a brute force search completely feasible. So the goal of the exercise is probably to make you implement at ...

1

No, not all curves are created equal. For one thing, the number of points on an elliptic curve defined over $\mathbf{F}_p$ varies in the interval $[p+1-2\sqrt{p},p+1+2\sqrt{p}]$ (Hasse's Inequality). There are also weak instances which must be avoided, the most catastrophic being when the number of points on the curve is exactly equal to $p$ (anomalous ...

1

If you want to reduce integers modulo that specific prime (and I assume you have checked whether $p = 2^{256}-2^{32}-2^9-2^8-2^7-2^6-2^4-1$ is prime or not), I would suggest you don't use the Solinas algorithms, but instead a different one geared towards modulii of the form $2^n - c$ for small $c$. The identity underlying this operation is actually fairly ...

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