Leveraging the hardness of dihedral coset problem for quantum cryptography

The dihedral coset problem (DCP) that comes from the hidden subgroup problem over dihedral group is one of the fundamental problems in quantum computation, and its hardness has become a promising cryptographic assumption of post quantum cryptography. In this work, we carry out a quantum cryptographic scheme based on dihedral coset states, which is a novel quantum cryptography that not only exploits the principles of quantum physics but also depends on the post-quantum hardness of DCPNℓ, where ℓ is the number of samples of DCP states and N is the modulus. Specifically, we propose a bipartite quantum key agreement protocol based on dihedral coset states, and by using it we demonstrate a quantum secure communication scenario that ⌊ ℓ/ 4 ⌋ bits of information can be transmitted securely. Finally, we discuss the security analysis of our proposal under the optimal measurement attack and show that the proposal can achieve the maximum secrecy capacity with information-theoretic security under the constraint of m= Θ(log N- 4) for the large N, where m denotes the number of DCP states transmitted in the quantum channel.