  In this paper, we present a new diverse class of post-quantum group-based
Digital Signature Schemes (DSS). The approach is significantly different from
previous examples of group-based digital signatures and adopts the framework of
group action-based cryptography: we show that each finite group defines a group
action relative to the semidirect product of the group by its automorphism
group, and give security bounds on the resulting signature scheme in terms of
the group-theoretic computational problem known as the Semidirect Discrete
Logarithm Problem (SDLP). Crucially, we make progress towards being able to
efficiently compute the novel group action, and give an example of a
parameterised family of groups for which the group action can be computed for
any parameters, thereby negating the need for expensive offline computation or
inclusion of redundancy required in other schemes of this type.

Cryptography and Security