# What is the current state of the Conjugacy Search Problem in Matrix and Permutation Groups?

It results that I have come with a mathematical approach to solve the CSP (Conjugacy Search Problem) where the platform group $$G$$ is either a permutation group or a Matrix Group.

From my part I studied non-commutative asymmetric protocols and cryptosystems, some of them based on the decomposition problem, factorization-search, the word problem or CSP. Normally, the decomposition and factorization-search problems are reducible to the CSP. That's why is so important to analyze the solvability of CSP in the platform group $$G$$.

For example, many authors use a group $$G$$ which is a Braid Group to implement their cryptographic protocols where the underlying problem depends on the CSP. The matrix algebra obtained from using Braids would make this algorithm useful. A faithful linear representation on $$\phi : B_n \to GL(n,F_q)$$ would do it in case of Braids. On [1] these techniques are commented, besides explaining how to solve various non-commutative protocols where $$G=B_n$$.

Q: Is there any cryptographic scheme based on the CSP using permutation or matrix groups as the platform group?

Q: Is the CSP still considered an interesting problem on the cryptographic community nowadays?

P.D : I included the tag "hard-problem" but it doesn't specify what content it makes reference. Feel free to remove or adapt any tag.