Title: Public-key cryptosystem based on quantum BCH codes and its quantum digital signature

Authors: Haiqing Han; Siru Zhu; Qin Li; Xiao Wang; Yutian Lei; Yuwei Zhang

Addresses: School of Computer, Wuhan University, Wuhan 430072, Hubei, China; School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, Hubei, China ' Air Force Early Warning Academy of PLA, Wuhan City 430072, Hubei Province, China ' School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, Hubei, China ' School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, Hubei, China ' School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, Hubei, China ' School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, Hubei, China

Abstract: There is a security threat to the traditional cryptography because of the emergence of quantum computation. Quantum computers can break through many cryptosystems based on mathematical puzzles. The post-cryptography has been established for the sake of the security. It has been proved that McEliece public-key cryptosystem based on error-correcting codes can resist quantum attacks. In this paper, several new generating algorithms of the quantum Bose-Chaudhuri-Hocquenghem (BCH) codes have been proposed, and the quantum BCH codes can correct the errors including bit-flip and phase-flip. At the same time, the quantum McEliece public-key cryptosystem and quantum Niederreiter public key cryptosystem have been designed by us on the basis of quantum BCH codes in this paper, and their encryption and decryption procedures are created in detail. Our cryptosystem not only retains the advantages of postquantum computation, but also can encrypt or decrypt in quantum state. From the perspective of computational complexity theory, both cryptosystems can resist the attacks of Shor algorithm and Grover algorithm very well. The Niederreiter classical digital signature is designed by us according to the structure characteristics of quantum BCH codes.

Keywords: CSS construction; quantum BCH codes; public key cryptosystem on error correcting codes; post-quantum attacks; quantum digital signatures.

DOI: 10.1504/IJSN.2020.111131

International Journal of Security and Networks, 2020 Vol.15 No.4, pp.197 - 205

Received: 16 Nov 2019
Accepted: 06 Jan 2020

Published online: 26 Oct 2020 *

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