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.
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.
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 existing certificateless signcryption schemes were designed mainly based on the traditional public key cryptography, in which the security relies on the hard problems, such as factor decomposition and discrete logarithm. However, these problems will be easily solved by the quantum computing. So the existing certificateless signcryption schemes are vulnerable to the quantum attack. Multivariate public key cryptography (MPKC), which can resist the quantum attack, is one of the alternative solutions to guarantee the security of communications in the post-quantum age. Motivated by these concerns, we proposed a new construction of the certificateless multi-receiver signcryption scheme (CLMSC) based on MPKC. The new scheme inherits the security of MPKC, which can withstand the quantum attack. Multivariate quadratic polynomial operations, which have lower computation complexity than bilinear pairing operations, are employed in signcrypting a message for a certain number of receivers in our scheme. Security analysis shows that our scheme is a secure MPKC-based scheme. We proved its security under the hardness of the Multivariate Quadratic (MQ) problem and its unforgeability under the Isomorphism of Polynomials (IP) assumption in the random oracle model. The analysis results show that our scheme also has the security properties of non-repudiation, perfect forward secrecy, perfect backward secrecy and public verifiability. Compared with the existing schemes in terms of computation complexity and ciphertext length, our scheme is more efficient, which makes it suitable for terminals with low computation capacity like smart cards.
The threshold proxy signcryption can implement signature and encryption simultaneously in one logical step, and can be used to realize the decentralized protection of the group signature key, so it is an efficient technology for network security. Currently, most of the existing threshold proxy signcryption schemes are designed based on the traditional public key cryptosystems, and their security mainly depends on the difficulty of the large integer decomposition and the discrete logarithm. However, the traditional public key cryptosystems cannot resist the quantum computer attack, which makes the existing threshold proxy signcryption schemes based on traditional public key cryptosystems insecure against quantum attacks. Motivated by these concerns, we proposed a threshold proxy signcryption scheme based on Multivariate Public Key Cryptosystem (MPKC) which is one of the quantum attack-resistent public key algorithms. Under the premise of satisfying the threshold signcryption requirements of the threshold proxy, our scheme can not only realize the flexible participation of the proxy signcrypters but also resist the quantum computing attack. Finally, based on the assumption of Multivariate Quadratic (MQ) problem and Isomorphism Polynomial (IP) problem, the proof of the confidentiality and the unforgeability of the proposed scheme under the random oracle model is given.
Identity-based signcryption schemes based on large integer factorization and discrete logarithm problems were considered to be insecure for the quantum computer attack. Thus, choosing a quantum-resist platform and constructing secure schemes based on new hard assumptions are challenges. In this paper, we propose an alternative scheme - an identity-based signcryption on lattice, which does not need to rely on a trapdoor. Meanwhile, our scheme achieves IND-CCA2 and sUF-CMA security, and it is also secure against the current quantum algorithm attacks based on LWE problem for lattice. Furthermore, we demonstrate that the newly proposed scheme has much shorter secret key size, and higher speeds in signcryption and unsigncryption stages, compared with some exiting identity-based signcryption schemes.
New developments in quantum computing have made people worry that current security methods could be broken by quantum attacks. Some mathematical problems are hard to solve, which is how traditional encryption methods like RSA and ECC keep their secrets safe. However, quantum computers might be able to solve these issues a lot faster than regular computers, which makes these methods less safe. Because of this threat, experts have been working hard to make post-quantum cryptography methods that quantum computers can't break. These methods are made to stand up to the strength of quantum algorithms and protect the privacy, integrity, and validity of private data even when quantum attackers are present. Lattice-based cryptography is a potential method for post-quantum encryption. Its security comes from the difficulty of certain lattice problems. Lattice-based methods are thought to be safe from threats from both traditional and quantum computers because they offer good security promises. Lattice-based cryptography is a flexible way to build different types of cryptographic primitives, like encryption, digital signatures, and key sharing protocols. The study of code-based cryptography, which is based on how hard it is to decode some error-correcting codes, is another important advance. Code-based methods have been around for a long time and have been studied a lot, which makes them a good choice for security after quantum computing. Code-based cryptography is also easy to use and has strong security features, which makes it a good choice for real-world situations. Multivariate polynomial cryptography is another possible choice for cryptography after quantum computing. The safety of this method depends on how hard it is to solve systems of multivariate polynomial problems. Multivariate polynomial methods might not be as secure as lattice-based or code-based cryptography, but they are interesting options for some situations and places with limited resources.
In this paper, we discuss the challenges of quantum computing to traditional cryptography and the latest development of post-quantum cryptography as a coping strategy. As quantum computing advances, cryptographic algorithms that rely on the complexity of classical computers, such as RSA and ECC, are at risk of failing, which has prompted the cryptography community to seek new encryption solutions. Post-quantum cryptography focuses on encryption technology and develops resistance to quantum computing attacks. It studies encryption schemes based on lattice theory, multivariate polynomials, coding theory, and hash functions. In addition, lattice-based cryptography is critical. It builds multiple algorithms, including RLWE and NTRU, focusing on LWE and SIS issues, demonstrating strong potential in a quantum computing environment. In terms of signature algorithms, Dilithium and Falcon lattice-based schemes are the focus of standardization. In the simulation analysis of these algorithms, we evaluated their security, efficiency, and compatibility, laying the theoretical and practical foundation for the cryptosystem transformation in the post-quantum era.