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Anti-Quantum Signcryption Scheme Based on Niederreiter Cryptosystem

WANG Zhong, HAN Yiliang

Published May 1, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.19678/j.issn.1000-3428.0054712

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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.
The development of quantum technology is changing with each passing day. While bringing convenience to us, the security problems it brings cannot be underestimated. By studying the multivariate cryptography and coding cryptography in anti-quantum cryptography, the core mapping of the improved version of Simple Matrix scheme is modified by LRPC code, which combines the MQ problem and the decoding difficulty problem, effectively reduces the ciphertext expansion rate and realizes the flexible choice of LRPC codes. Based on the improvement of the trapdoor, a generalized signcryption scheme against quantum is proposed, which proves to meet the security of IND-CCA2 and the security of EUF-CMA. It can realize the adaptive conversion between signature, encryption, signcryption and normal mode, adapt to more complex network communication, and show strong survivability in the post-quantum era.
Ensuring the security of transmitted content is an important task in network communication. Signcryption technology combines signature and encryption operations in a single step to achieve message authentication and confidentiality. In practical applications, users are usually in different cryptographic systems, the ordinary signcryption technology cannot realize communication between two different cryptographic systems. And the ciphertext structure of the existing signcryption schemes is relatively complex, signcryption is not efficient. Therefore, in order to solve the problem of efficient communication between different cryptosystems and ensure quantum security, this paper proposes a lattice-based efficient heterogeneous signcryption scheme for secure network communications. This signcryption scheme accomplishes signcryption through matrix operations and hash functions, which avoids complex signcryption structures, efficiently realizes bidirectional message communication between identity-based cryptosystems and certificateless cryptosystems.
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.
With the fast advancement in quantum computing, conventional cryptography is facing great challenges, with quantum algorithms like Shor’s algorithm and Grover’s algorithm threatening to break most widely used cryptosystems and hashing algorithms. Cryptosystems that use public-key cryptography, such as RSA, have proven vulnerable to quantum attacks. This presents a high threat to digital communication, as it can compromise modern communication systems’ confidentiality, authenticity, and integrity. On the other hand, modern cryptosystems treat digital signatures and encryption as two separate operations, adopting the sign-then-encrypt method for securing communication, which results in significant computational cost and overhead. This paper proposes a Quantum Signcryption tool to solve these problems, offering a system enhanced by quantum technology and secured against quantum threats. This system combines the functions of encryption and digital signatures into a single process to function as an efficient and secure tool for future quantum communication, with an average end-to-end execution time of 20.615s, consuming 11092 KBs of memory.
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.
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.