The Hidden Subgroup Problem and Post-quantum Group-based Cryptography
This is an incremental review for researchers in cryptography and quantum computing, addressing security challenges in post-quantum cryptography.
The paper tackles the Hidden Subgroup Problem (HSP) in the context of post-quantum group-based cryptography, reviewing its relationship with computational problems and noting that efficient algorithms for solving HSP in infinite groups are not yet known.
In this paper we discuss the Hidden Subgroup Problem (HSP) in relation to post-quantum group-based cryptography. We review the relationship between HSP and other computational problems discuss an optimal solution method, and review the known results about the quantum complexity of HSP. We also overview some platforms for group-based cryptosystems. Notably, efficient algorithms for solving HSP in such infinite group platforms are not yet known.