2018/05/25 by Upendra Kapshikar, Kapshikar, Upendra · 1 citation
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #Cryptography and Security (cs.CR) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1805.09972
openalex publication_date 2018/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.