# Tag Info

Accepted

### How to determine the order of an elliptic curve group from its parameters?

There is a rather deep polynomial-time algorithm for counting the $\mathbb F_q$-rational points of an elliptic curve published by René Schoof in 1985 (with subsequent improvements by Noam Elkies and A....

### Why are finite groups used in cryptography?

Can someone explain why is that the case? Cryptosystems based on finite sets have two very nice properties: There is an upper bound to the size of all involved mathematical objects. This also allows ...
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Accepted

### Which properties of a group are used in the steps of Diffie Hellman?

I’m trying to understand which properties of a group are used in DHKE at each step. Actually, you can implement a DH-style operation in any semigroup; you need closure, and you need associativity (...
Accepted

### Do $v_1=\alpha\cdot r_1$ and $v_2=\alpha\cdot r_2$ leak information about $\alpha$

Question: Given $n$ values $v_1=\alpha \cdot r_1 \bmod p,..., v_n=\alpha \cdot r_n \bmod p$ for a large $n$ can the adversary learn the value $\alpha$? Answer: assuming that the $r_i$ values are ...

Accepted

Accepted

Accepted

### How is it decided if $G_1$ and $G_2$ are two “additive” or “multiplicative” cyclic groups?

Notation is basically a free choice of the author, as they describe functionally the same. And there is no fixed definition for this. However, common practice in mathematical publications is: ...
Cyclic group of prime order q such that the DLP is hard A simple technique to form a cyclic group $G$ of prime order $q$ such that the underlying discrete logarithm problem (DLP) is (conjecturally) ...
The obvious way to create such a hash function would be to first define a hash function $H$ (distinct from $H_1$) that generates as output an integer in the range $[2, q]$, and then define \$H_2(x) = H(...