# Questions tagged [group-theory]

Groups are an abstract algebraic concept based on a set and a group law (a binary function which closes the set).

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

According to wiki's definition of Bilinear pairing… Let $G_1$ and $G_2$ be two additive cyclic groups of prime order $q$, and $G_T$ another cyclic group of order $q$ written multiplicatively. A ...
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### Additive proof of discrete log?

Let's say someone has $K$, and I want to prove to them that I know $k$ such $K = k*g$ (where $g$ is some sort of group element). I can use a Schnorr signature. Is there some protocol for mergable ...
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### How to find g in Factoring-Based Trapdoor Hash Function

Please explain how to find a value of $g$ if $p,q$ are safe primes having $p'=(p-1)/2$ and $q'=(q-1)/2$ are also primes $n=p*q$ $\lambda(𝑛) = \operatorname{lcm}(𝑝 − 1, 𝑞 − 1) = 2𝑝'𝑞'$. How to ...
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### in Bilinear pairings, what is the difference between Type 2 and Type 3?

in Bilinear pairings, what is the difference between Type 2 and Type 3? I understand in Type 2, there exists an efficiently computable homomorphic function $\phi : G_2 \rightarrow G_1$ , which is not ...
If there a proof in the literature which says the CONF Problem is equivalent to solving the discrete log ? Let $g$ be a generator of a cyclic group $\mathbb{G}$ of prime order $q$ CONF problem: ...