Public key cryptography based on twisted dihedral group algebras
This work addresses the need for novel cryptographic schemes, but it appears incremental as it builds on existing group algebra concepts without claiming broad breakthroughs.
The paper tackles the problem of designing public-key cryptography by proposing a new approach based on twisted dihedral group algebras, introducing a key exchange protocol and a probabilistic public-key scheme, and implementing a proof-of-concept key encapsulation mechanism.
In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, we introduce a new $2$-cocycle $α_λ$ to twist the dihedral group algebra. Using the ambient space $\mathbb{F}^{α_λ} D_{2n}$, we then introduce a key exchange protocol and present an analysis of its security. Moreover, we explore the properties of the resulting twisted algebra $\mathbb{F}^{α_λ}D_{2n}$, exploiting them to enhance our key exchange protocol. We also introduce a probabilistic public-key scheme derived from our key-exchange protocol and obtain a key encapsulation mechanism (KEM) by applying a well-known generic transformation to our public-key scheme. Finally, we present a proof-of-concept implementation of the resulting key encapsulation mechanism.