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Lecture notes in networks and systems

A Survey on Development of Post-quantum Cryptographic Schemes

Alvary Kefas Kwala, Alpna Mishra, Shri Kant

Published Jan 1, 2025• 1 citation
Publisher
DOI
10.1007/978-981-96-3358-6_34

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Public-key cryptography provides security for digital systems and communication. Traditional cryptographic solutions are constantly improved, e.g., to suppress brute-force attacks. However, Shor’s algorithm suited for quantum computers can break the bedrock of most currently used systems, i.e., the RSA problem and discrete logarithm problem. Post-quantum cryptography can withstand attacks carried out by quantum computers. Several families of post-quantum systems exist; one of them is isogeny-based cryptography. As a main contribution, in this paper, we provide a survey of chosen, fundamental isogeny-based schemes. The target audience of this review is researchers interested in practical aspects of this field of cryptography; therefore the survey contains exemplary implementations. Our goal was not to develop an efficient implementation, but to provide materials that make it easier to analyze isogeny-based cryptography.
Commitment schemes represent foundational cryptographic primitives enabling secure verification protocols across diverse applications, from blockchain systems to zero-knowledge proofs. This paper presents a systematic survey of vector, polynomial, and functional commitment schemes, analyzing their evolution from classical constructions to post-quantum secure alternatives. We examine the strengths and limitations of RSA-based, Diffie–Hellman, and lattice-based approaches, highlighting the critical shift toward quantum-resistant designs necessitated by emerging computational threats. The survey reveals that while lattice-based schemes (particularly those using the Short Integer Solution problem) offer promising security guarantees, they face practical challenges in proof size and verification efficiency. Functional commitments emerge as a powerful generalization, though their adoption is constrained by computational overhead and setup requirements. Key findings identify persistent gaps in adaptive security, composability, and real-world deployment, while proposed solutions emphasize optimization techniques and hybrid approaches. By synthesizing over 90 research works, this paper provides both a comprehensive reference for cryptographic researchers and a roadmap for future developments in commitment schemes, particularly in addressing the urgent demands of post-quantum cryptography and decentralized systems.