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3. Foundations

More general group-theoretic questions with implications in the field.

    1. Applications of infinite non-abelian groups to cryptography


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      Problem 3.1.

      Several cryptanalytic methods against group-based cryptography suggest possible use cases for infinite non-abelian groups; for example, non-Hopfian groups. We would like to develop tools to understand how these infinite objects can fit into a cryptographic context, and whether their use can be used to address some of the cryptanalytic methods deployed against group-based cryptography.

        • Cryptographic building blocks from problems in group theory


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          Problem 3.2.

          We would like to use computational problems in group theory to derive fundamental cryptographic objects including one-way functions and multilinear maps.

            • Computational problems from graph groups


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              Problem 3.3.

              It is known that it is possible to establish correspondence between certain NP-hard graph problems and problems in group theory; we would like to expand our portfolio of such problems.

                  Cite this as: AimPL: Post-quantum group-based cryptography, available at http://aimpl.org/postquantgroup.