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2. Design

Open problems relating to the design of protocols in group-theoretic cryptography.

    1. Advanced digital signature functionality from group theory

          The connection between SDLP and group actions suggests the availability of generic group-action tools to build more efficient signatures, or signatures with more specialised properties.

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      Problem 2.1.

      We would like to use generic group-action tools to build ring signatures, blind signatures, threshold signatures and more. We would also like to apply the "twist" technique present in similar isogeny schemes to improve the memory performance of group-based digital signatures.

        • Creation of challenge instances


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          Problem 2.2.

          Across the various group-based protocols there is a general lack of precision on which parameter specification. As the field matures we should make available challenge instances of each protocol.

            • Implementation of group-based cryptography


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              Problem 2.3.

              In general very little work exists on efficient implementation of group-based protocols; over time we would like to build up a software library of such implementations.

                • Methods of key establishment from group theory


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                  Problem 2.4.

                  Generally speaking the field does not seem to offer methods of key establishment. It remains open to construct standard key exchange protocols as well as more complicated multi-party variants.

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