McEliece-type Cryptosystems over Quasi-cyclic Codes

05/25/2018

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by   Upendra Kapshikar, et al.

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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 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 1/m quasi-cyclic codes, with small size and large minimal degree of the automorphism group.