McEliece-type Cryptosystems over Quasi-cyclic Codes
This work addresses the need for quantum-resistant cryptography, offering a potential solution for secure communications in a post-quantum era, though it appears incremental as it builds on existing McEliece-type frameworks.
The authors tackled the problem of constructing quantum-secure cryptosystems by proposing a new variant of the Niederreiter cryptosystem over rate (m-1)/m quasi-cyclic codes, which resists quantum Fourier sampling due to indistinguishability of the hidden subgroup, and also presented a class of 1/m quasi-cyclic codes with specific automorphism group properties.
In this thesis, we study algebraic coding theory based McEliece-type cryptosystems over quasi-cyclic codes. The main goal of this thesis is to construct a cryptosystem that resists quantum Fourier sampling making it quantum secure. We propose a new variant of Niederreiter cryptosystem over rate $\frac{m-1}{m}$ quasi-cyclic codes which is secure against quantum Fourier sampling due to indistinguishability of the hidden subgroup. The proof of indistinguishability is achieved due to two constraints over automorphism group; small size and large minimal degree. Apart from this cryptosystem, we also present a class of $\frac{1}{m}$ quasi-cyclic codes, with small size and large minimal degree of the automorphism group.