AAG with a generalized Heisenberg group is solvable in PTIME

What is it about?

A common encryption scheme called AAG allows for a number of different implementations by choosing a specific platform group. Tests with specific attacks suggested that AAG might be secure using generalized Heisenberg groups. We showed that a direct attack on the algebraic question related to AAG allows us to generate a solution in PTIME. As a result, AAG is not secure with a generalized Heisenberg group platform.

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Why is it important?

We developed an algorithm, and so gave a constructive proof, to the Subgroup Restricted Simultaneous Conjugacy Search Problem in generalized Heisenberg groups. Thus, we showed that AAG should not be used for security with that specific class of groups. Previous papers suggested resistance to other common attacks. Similar linear algebra types of attacks might be useful for similar platform groups that are also resistant to common attacks (like length based attacks).