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McEliece and Niederreiter cryptosystems are robust and versatilecryptosystems. These cryptosystems work with many linear error-correctingcodes. They are popular these days because they can be quantum-secure. In thispaper, we study the Niederreiter cryptosystem using non-binary quasi-cycliccodes. We prove, if these quasi-cyclic codes satisfy certain conditions, thecorresponding Niederreiter cryptosystem is resistant to the hidden subgroupproblem using weak quantum Fourier sampling. Though our work uses the weakFourier sampling, we argue that its conclusions should remain valid for thestrong Fourier sampling as well.

Niederreiter cryptosystems using quasi-cyclic codes that resist quantum Fourier sampling