Shor's quantum algorithm and other efficient quantum algorithms can break many public-key cryptographic schemes in polynomial time on a quantum computer. In response, researchers proposed postquantum cryptography to resist quantum computers. The multivariate cryptosystem (MVC) is one of a few options of postquantum cryptography. It is based on the NP-hardness of the computational problem to solve nonlinear equations over a finite field. Recently, Wang et al. (2018) proposed a MVC based on extended clipped hopfield neural networks (eCHNN). Its main security assumption is backed by the discrete logarithm (DL) problem over Matrics. In this brief, we present quantum cryptanalysis of Wang et al. 's eCHNN-based MVC. We first show that Shor's quantum algorithm can be modified to solve the DL problem over Matrics. Then we show that Wang et al. 's construction of eCHNN-based MVC is not secure against quantum computers; this against the original intention of that multivariate cryptography is one of a few options of postquantum cryptography.
Shor's quantum algorithm and other efficient quantum algorithms can break many public-key cryptographic schemes in polynomial time on a quantum computer. In response, researchers proposed postquantum cryptography to resist quantum computers. The multivariate cryptosystem (MVC) is one of a few options of postquantum cryptography. It is based on the NP-hardness of the computational problem to solve nonlinear equations over a finite field. Recently, Wang et al. (2018) proposed a MVC based on extended clipped hopfield neural networks (eCHNN). Its main security assumption is backed by the discrete logarithm (DL) problem over Matrics. In this brief, we present quantum cryptanalysis of Wang et al. 's eCHNN-based MVC. We first show that Shor's quantum algorithm can be modified to solve the DL problem over Matrics. Then we show that Wang et al. 's construction of eCHNN-based MVC is not secure against quantum computers; this against the original intention of that multivariate cryptography is one of a few options of postquantum cryptography.
The security of current public-key cryptosystems relies on the hardness of factoring large integers or solving discrete logarithm problems. However, these mathematical problems can be solved in polynomial time using a quantum computer. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. In this expository article, we give an overview of recent research on post-quantum cryptography. In particular, we describe the construction and security of multivariate polynomial cryptosystems and lattice-based cryptosystems, which are the main candidates of post-quantum cryptography.
Quantum computation is a new computational model based on quantum mechanical principle.Shor invented the polynomial time algorithms for the prime factorization and discrete logarithm problem, which indicated that the cryptosystems based on them are totally unsafe in the quantum world.Grover constructed an algorithm that finds a solution in only O( 2 n )steps whereas the exhaustive search algorithm needs O( 2n ) steps on average.In this paper we investigate the cryptanalysis of a new cryptography problem----multivariate permutation problem (MPP), which could be used to design public-key cryptosystem, with the help of the two quantum algorithms.Specially, we discuss the strength of a private key of the REESSE1+ public-key cryptosystem, whose security is based on the hardness of MPP.Besides, some suggestions are also given about the implementation of the REESSE1+.
Much of the assumed safety and security of classical cryptographic building blocks depends on the hardness of number-theoretical problems. However, Shor's algorithm proves that conventional cryptographic systems are no longer secure under quantum systems. As a response to this challenge, researchers started to develop a new cryptographic method known as post-quantum cryptography (PQC), which is based on hard computational problem that can resist the quantum threats. The multivariate public-key cryptography (MPKC) is one such candidate. The theoretical security of MPKC comes from the intractability of the MQ problem, which is believed to be NP-hard. Herein, we analyze the security of MQDSS signature scheme proposed by Chen et al. We investigate the proof of security of MQDSS, assuming that the malicious party can access to the quantum resources. We demonstrate that in its current state, MQDSS has quite a few insecurities in the quantum setting. In response to the proposed threats, we pitch possible modifications to MQDSS. We emphasize that our proposed security threats do not restrict themselves to MQDSS, and can be extended to other MPKC and PQC based cryptographic primitives.
This chapter covers the potential use of quantum algorithms for cryptanalysis, that is, the breaking and weakening of cryptosystems. We discuss Shor’s algorithm for factoring and discrete logarithm, which render widely used public-key cryptosystems vulnerable to attack, given access to a sufficiently large-scale quantum computer. We present resource estimates from the literature for running Shor’s algorithm, and we discuss the outlook for postquantum cryptography, which aims to replace existing cryptosystems while being resistant to quantum attack. We also cover quantum approaches for weakening the security of cryptosystems based on Grover’s search algorithm.
Abstractly, the fast development of quantum computing is a threat to classical public-key cryptographic infrastructures.Asymmetric algorithms (which are widely used and include RSA and Elliptic Curve Cryptography (ECC)) are susceptible to the Shor algorithm, which can break them in a time-polynomial manner.This paper will give a detailed comparative study of Post-Quantum Cryptography (PQC) schemes founded on discrete algebraic structures such as lattice-based, code-based, hash-based, and multivariate polynomials based cryptosystems.These paradigms are systematically assessed according to computational complexity, key and ciphertext sizes, security reduction assumptions, and how they can be deployed on large scale networks.The NIST-standardized algorithms, which are the focus of our analysis, are ML-KEM (CRYSTALS-Kyber), ML-DSA (CRYSTALS Dilithium), FN-DSA (Falcon), and SLH-DSA (SPHINCS+).We also consider hybrid cryptography transitional measures to provide backward compatibility and security guarantee in the process of migrating the classical to quantum-resistant systems.As we found, the current state of lattice-based schemes provides the most desirable ratio of security to performance in large-scale applications, although, in the long run, code-based and multivariate schemes are necessary as their complements.
Quantum computing is a transformational technology once implemented, capable of addressing problems far beyond the capacity of classical computers. But this progress is also a real challenge to the core of today's modern security. Traditional cryptographic algorithms, such as those based on RSA, ECC, and Diffie-Hellman key exchange, are based on the computational hardness of problems such as prime factorization and discrete logarithms that quantum algorithms solve in polynomial time. As a particular research interesting example, with Shor's Algorithm one can factorize large numbers efficiently, rendering insecure the majority of public key cryptosystems used nowadays. This urgently demands a reevaluation of existing encryption schemes in the context of a post-quantum world. In this paper, we take a closer look at the threats that quantum computers pose to classical security infrastructure including encryption scheme and explore the impact that quantum computation can have on current cryptographic schemes. It calculates the cost in terms of symmetric and asymmetric security, accounting for effects of both Shor's and Grover's algorithms. Symmetric key systems such as AES are also harder hit—Grover's algorithm can give only a quadratic speedup here—but they do need to double key sizes for a sufficient level of post-quantum security. In reaction to those threats, the paper investigates nextgeneration post-quantum cryptographic (PQC) solutions resistant to quantum cryptanalysis. Lattice-based cryptosystems, hash-based signature schemes, multivariate polynomial systems, and code-based cryptosystems are some of the candidates that are being considered in international standardization work, including especially at NIST. In this paper, we compare those alternatives for security, performance, scalability, and feasibility of implementation in real system. An important aspect of this contribution is a comparative study of traditional and post-quantum cryptographic protocols in the context of a number of cybersecurity applications, including secure communications, blockchain networks and IoT contexts. It also covers the quantum readiness timeline and transitional issues, such as backward compatibility, standardization lag and the associated increased computational overhead. Through a mitigated risk evaluation and cryptanalytic attack simulation based on quantum-inspired algorithms, this analysis emphasizes the need to prepare ourselves against quantum-induced security issues. It provides strategic guidance to organizations as they plan for the post-quantum future, stressing cryptographic agility, hybrid encryption models and real-time threat monitoring. Ultimately, the results of this work add to the worldwide conversation on establishing secure systems within the digital age of quantum computing and recommend proactive migration plans for the integrity, confidentiality, and trust one should have in the future cyber world.