Niederreiter cryptosystems using quasi-cyclic codes that resist quantum Fourier sampling
This work provides a quantum-resistant cryptographic method for secure communications, though it appears incremental as it builds on existing Niederreiter frameworks with specific code modifications.
The authors tackled the problem of quantum attacks on Niederreiter cryptosystems by proving that using non-binary quasi-cyclic codes with certain conditions makes the system resistant to hidden subgroup problems via weak quantum Fourier sampling, with implications for strong sampling as well.
McEliece and Niederreiter cryptosystems are robust and versatile cryptosystems. These cryptosystems work with many linear error-correcting codes. They are popular these days because they can be quantum-secure. In this paper, we study the Niederreiter cryptosystem using non-binary quasi-cyclic codes. We prove, if these quasi-cyclic codes satisfy certain conditions, the corresponding Niederreiter cryptosystem is resistant to the hidden subgroup problem using weak quantum Fourier sampling. Though our work uses the weak Fourier sampling, we argue that its conclusions should remain valid for the strong Fourier sampling as well.