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International Conference on Internet Technology and Applications

A Construction Method of Niederreiter Public-Key Cryptosystem Based on Quantum LDPC Codes

Dong Cao, Yaoliang Song

Published Aug 1, 2010• 0 citations
Publisher

Abstract

Quantum public-key cryptosystem includes unconditionally secure quantum public-key cryptographic algorithm and computationally secure quantum public-key cryptographic algorithm. This paper presents a quantum Niederreiter public-key cryptosystem by using quantum stabilizer LDPC codes. Constructed key based on quantum LDPC codes directly. Take advantage of the sparsity of LDPC codes. Compared with McEliece public-key cryptosystem, Encoding complexity is reduced. Its security relies on the fact that NPC problem can not be solved on quantum Turing machines.

DOI
10.1109/itapp.2010.5566239

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Quantum public-key cryptosystem includes unconditionally secure quantum public-key cryptographic algorithm and computationally secure quantum public-key cryptographic algorithm. This paper presents a quantum Niederreiter public-key cryptosystem by using quantum stabilizer LDPC codes. Constructed key based on quantum LDPC codes directly. Take advantage of the sparsity of LDPC codes. Compared with McEliece public-key cryptosystem, Encoding complexity is reduced. Its security relies on the fact that NPC problem can not be solved on quantum Turing machines.
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.
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.
The McEliece cryptosystem is one of the best-known (classical) public-key cryptosystems, which is based on algebraic coding theory. In this paper, we present a quantum analogue of the classical McEliece cryptosystem. Our quantum McEliece public-key cryptosystem is based on the theory of stabilizer codes and has the key generation, encryption and decryption algorithms similar to those in the classical McEliece cryptosystem. We present an explicit construction of the quantum McEliece public-key cryptosystem using Calderbank-Shor-Steane codes based on generalized Reed-Solomon codes. We examine the security of our quantum McEliece cryptosystem and compare it with alternative systems.
To address security issues of network communication in the post-quantum era,this paper studies the Niederreiter cryptosystem in code-based cryptography,and combines the double public key cryptographic scheme based on the improved Niederreiter scheme with the Xinmei signature scheme to construct an anti-quantum signcryption scheme.Security analysis results show that the proposed signcryption scheme can meet the security requirements of IND-CPA and EUF-CMA,and can achieve excellent defense against direct decoding attacks and ISD attacks.Compared with signcryption schemes that implement encryption after signing,the proposed scheme can reduce the amount of ciphertext by 50%,providing confidentiality and unforgeable security for network communication in the post-quantum era.
Abstract. This paper presents a new paradigm of cryptography, quantum public-key cryptosystems. In quantum public-key cryptosystems, all parties including senders, receivers and adversaries are modeled as quantum (probabilistic) poly-time Turing (QPT) machines and only classical channels (i.e., no quantum channels) are employed. A quantum trapdoor one-way function, f, plays an essential role in our system, in which a QPT machine can compute f with high probability, any QPT machine can invert f with negligible probability, and a QPT machine with trapdoor data can invert f. This paper proposes a concrete scheme for quantum public-key cryptosystems: a quantum public-key encryption scheme or quantum trapdoor one-way function. The security of our schemes is based on the computational assumption (over QPT machines) that a class of subset-sum problems is intractable against any QPT machine. Our scheme is very efficient and practical if Shor’s discrete logarithm algorithm is efficiently realized on a quantum machine.