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 does the wider cryptographic community view non-abelian group based cryptography?

Is there perhaps some neural expository article on crypto systems based on non-abelian groups? I've gleaned that Anshel–Anshel–Goldfeld key exchange is the most well-known cryptographic algorithm ...
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Must the order of the groups in a bilinear map be the same?

I've been reading up on bilinear maps and their application to cryptography and one thing I keep seeing hasn't yet clicked. If $e:G_1\times G_2\to G_n$ is a bilinear map, $G_1,G_2,G_n$ are always ...
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Is there a group of prime order which could fit the CT-Computational Diffie-Hellman assumption?

I'm trying to choose a group that is hard under the Chosen-Target Computational Diffie-Hellman assumption, according to the definition in this paper, in order to implement the oblivious transfer ...
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Would the ability to efficiently find Discrete Logs have any impact on the security of RSA?

This answer makes the claim that the Discrete Log problem and RSA are independent from a security perspective. RSA labs makes a similar statement: The discrete logarithm problem bears the same ...
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What exactly is the impact of the hidden subgroup problem on cryptography?

I understand my group theory (allegedly), so I can make partial sense of The Hidden Subgroup problem: Given a group $G$, a subgroup $H \leq G$, and a set $X$, we say a function $f : G \Rightarrow ...