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Quantum Information and Computation

Quantum McEliece public-key cryptosystem

Hachiro Fujita

Published Mar 1, 2012• 17 citations
Publisher

Abstract

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.

DOI
10.26421/qic12.3-4-1

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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.
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 paradigm of quantum computation has led to the development of new algorithms as well variations on existing algorithms. In particular, novel cryptographic techniques based upon quantum computation are of great interest. Many classical encryption techniques naturally translate into the quantum paradigm because of their well-structured factorizations and the fact that they can be phased in the form of unitary operators. In this work, we demonstrate a quantum approach to data encryption and decryption based upon the McEliece cryptosystem using Reed-Muller codes. This example is of particular interest given that post-quantum analyses have highlighted this system as being robust against quantum attacks. Finally, in anticipation of quantum computation operating over binary fields, we discuss alternative operator factorizations for the proposed cryptosystem.
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.
A quantum cryptosystem based on algebraic codes, which uses single photons as quantum message carriers, is given. The cryptosystem is equipped with authentication, data integrity, and non-repudiation. There is no need for a parallel classical channel since public conversation is omitted. Indeed by using a suitable algebraic error-correcting code, Alice and Bob do not need to share a string of common bases. Therefore, they already share only one secret key for encryption. The secret key can be reused many times also in a noisy environment. The encryption and the decryption are similar, so the cryptosystem can be thought symmetric. Analysis shows that the cryptosystem is secure, low cost, and more practical compared with the previous ones.