In this paper, we present a simple bare-bones solution of a Zero-Knowledge authentication protocol which uses non-commutative algebra and a variation of the generalized symmetric decomposition problem (GSDP) as a one-way function. The cryptographic security is assured as long the GSDP problem is computationally hard to solve in non-commutative algebraic structures and belongs currently to the PQC category as no quantum computer attack is likely to exists.
In this paper, we present a simple bare-bones solution of a Zero-Knowledge authentication protocol which uses non-commutative algebra and a variation of the generalized symmetric decomposition problem (GSDP) as a one-way function. The cryptographic security is assured as long the GSDP problem is computationally hard to solve in non-commutative algebraic structures and belongs currently to the PQC category as no quantum computer attack is likely to exists.
Quantum computing presents a significant threat to traditional cryptographic protocols, particularly those relying on the hardness of factoring large integers and computing discrete logarithms, as quantum algorithms can solve these problems in polynomial time. With the advent of quantum computers capable of breaking current cryptographic schemes, the need for quantum-resistant cryptographic mechanisms has become increasingly urgent. In this paper, we focused on authentication, a critical security property, and reviewed various classical cryptographic techniques to this aim and their potential to resist quantum attacks. We present a (non-exhaustive) overview of the state of the art in quantum-resistant authentication, particularly through symmetric cryptography, digital signatures, and hardware-based approaches such as physical unclonable functions (PUFs). By offering a clear and focused analysis, we used this survey to bridge the gap between diverse academic communities and provide a foundation for future research in post-quantum authentication.
Shor’s quantum factoring algorithm and a few other efficient quantum algorithms break many clas-sical crypto-systems. In response, people proposed post-quantum cryptography based on computational problems that are believed hard even for quantum computers. However, security of these schemes against quantum attacks is elusive. This is because existing security analysis (almost) only deals with classical attackers and arguing security in the presence of quantum adversaries is challenging due to unique quan-tum features such as no-cloning. This work proposes a general framework to study which classical security proofs can be restored in the quantum setting. Basically, we split a security proof into (a sequence of) classical security reductions, and investigate what security reductions are “quantum-friendly”. We characterize sufficient conditions such that a classical reduction can be “lifted ” to the quantum setting. We then apply our lifting theorems to post-quantum signature schemes. We are able to show that the classical generic construction of hash-tree based signatures from one-way functions and and a more efficient variant proposed in [BDH11] carry over to the quantum setting. Namely, assuming existence of (classical) one-way functions that are resistant to efficient quantum inversion algorithms, there exists a quantum-secure signature scheme. We note that the scheme in [BDH11] is a promising (post-quantum) candidate to be implemented in practice and our result further justifies it. Actually, to obtain these results, we formalize a simple criteria, which is motivated by many classical proofs in the literature and is straightforward to check. This makes our lifting theorem easier to apply, and it should be useful elsewhere to prove quantum security of proposed post-quantum cryptographic schemes. Finally we demonstrate the generality of our framework by showing that several existing works (Full-Domain hash in the quantum random-oracle model [Zha12b] and the simple hybrid arguments framework in [HSS11]) can be reformulated under our unified framework. 1
The increasing advancement in quantum computing threatens the security of traditional cryptographic systems that underpin much of the modern world’s data protection. These systems rely heavily on the computational difficulty of problems like integer factorization (RSA) and elliptic curve discrete logarithms (ECC), which quantum computers could solve in polynomial time. As a result, there is an urgent need for cryptographic systems that remain secure even in the presence of quantum capabilities. Post-Quantum Cryptography (PQC) is the emerging field that aims to develop cryptographic protocols resistant to quantum-based attacks. This paper discusses the need for PQC, explores various candidate algorithms, reviews standardization efforts, and looks at the current challenges and future directions in the field.
In modern computer networks, cryptography is vital for preserving privacy, protecting sensitive information, and securing online communication. The mathematical problems that conventional encryption algorithms such as RSA and ECC depend on are tough for standard computers to tackle. Nonetheless, these traditional methods could be vulnerable to quantum assaults due to the rapid advancement of quantum computing. Post-quantum cryptography (PQC) refers to cryptographic methods designed to be secure against both classical and quantum computers. These algorithms rely on mathematical challenges believed to be resistant to quantum attacks, such as multivariate polynomial, hash, lattice, and code-based problems. This paper examines the necessity for post-quantum cryptography, the weaknesses of existing cryptographic systems, and the various categories of post-quantum algorithms.
A Zero-Knowledge Proof basically is a protocol between two parties, the Prover and the Verifier, that allows the Prover to convince the Verifier about the truthness of a non trivial statement without revealing any additional information. Zero Knowledge Proofs have found a lot of practical applications covering most of the protocols concerning about data privacy and protocol verification. Examples of that are anonymous cash or electronic voting. The possibility to have real quantum computers with a reasonable size in a near future is forcing the cryptographic community to devise new methods to provide security that resist quantum attacks. Most of the zero-knowledge protocols used nowadays are based on computational problems like the discrete logarithm problem that can no longer be considered hard, since there are known efficient ways to solve them with quantum algorithms. Cryptographic research about the quantum security of zero knowledge proofs started nearly 20 years ago in a very theoretical approach, but not many papers on that topic appeared since then. The goal of this thesis is writing a survey including the main concepts about quantum secure zero-knowledge protocols, the state-of-the-art both from the theoretical and practical approaches, and an exploration of their potential application areas. The survey will be a good starting document for further students willing to do research in this topic.
Abstract It is viewed as revolutionary technology, offering incredible potential in terms of computing power within different scientific and industrial sectors. Quantum computers provide remarkable computing power; however, they also present significant security risks to existing public-key cryptography systems used to secure digital communication, online banking systems, government, medical applications, cloud computing systems, and IoT systems. Security of commonly used encryption schemes like RSA, DH, and ECC depends on mathematical problems that are impossible for classical computers to solve but can be easily resolved with the help of powerful enough quantum computers by using Shor’s algorithm. Furthermore, Grover’s algorithm makes exhaustive search attacks much faster, thus effectively lowering the security level of symmetric encryption schemes since it provides the speed-up for brute-force attacks. Post-Quantum Cryptography (PQC) turned out to be an effective and scalable method to protect digital data from attacks using quantum computing. In contrast to quantum cryptography, which requires a special quantum communication channel, PQC uses classical cryptographic algorithms that cannot be broken down by either classical or quantum computer due to certain mathematical problems. This research paper offers an extensive exploration of post-quantum cryptography through the analysis of the development of quantum computing, weaknesses of current cryptographic techniques, and mathematics behind quantum-resistant algorithms. Moreover, this paper explores the major classes of PQC techniques such as lattice-based, code-based, hash-based, multivariate, and isogeny-based cryptography and provides details about their security and application. Moreover, the report gives an overview of the NIST Post-Quantum Cryptography Standardization Project and analyzes recent standardizations of quantum-proof algorithms to be utilized in future digital infrastructures. Keywords: Post-Quantum Encryption, Quantum Security, Quantum-Proof Public-Key Cryptography, Lattice-Based Security Protocols, ML-KEM Key Encapsulation Mechanism, ML-DSA Digital Signature Algorithm, NIST Post-Quantum Cryptography, Contemporary Cybersecurity, Secure Communications, Cryptographic Algorithms.