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Lecture notes in computer science

Security Comparisons and Performance Analyses of Post-quantum Signature Algorithms

Manohar Raavi, Simeon Wuthier, Pranav Chandramouli, Yaroslav Balytskyi, Xiaobo Zhou, Sang‐Yoon Chang

Published Jan 1, 2021• 51 citations
Publisher
DOI
10.1007/978-3-030-78375-4_17

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The advent of quantum computing presents a significant threat to the security of asymmetric cryptographic algorithms, necessitating the adoption of new cryptographic mechanisms resilient to quantum-based attacks. This need is particularly critical for applications that rely exclusively on public-key cryptography, such as digital signatures. This paper presents a comprehensive analysis of the performance of various post-quantum cryptographic algorithms, focusing specifically on NIST-standardized digital signature algorithms—SPHINCS+ and Dilithium—and their practical implementations. The study evaluates these algorithms across different programming languages to identify optimal environments for diverse applications. Comparative analyses with the widely used RSA algorithm reveal that the computational cost of adopting post-quantum cryptographic systems is relatively low. Notably, some post-quantum algorithms demonstrate performance advantages over classical RSA in specific scenarios.
Nowadays, we are surrounded by devices collecting and transmitting private information. Currently, the two main mathematical problems that guarantee security on the Internet are the Integer Factorization Problem and the Discrete Logarithm Problem. However, Shor's quantum algorithm can easily solve both problems. Therefore, research into cryptographic algorithms that run in classical computers and are resistant to quantum computers is extremely necessary. This area is known as post-quantum cryptography and usually studies asymmetric cryptography. By means of asymptotic analysis, the purpose of this paper is to provide an evaluation of security and its performance for the types of cryptographic systems considered safe against quantum attacks in the second-round NIST Post-Quantum Standardization Process, namely isogeny cryptosystems based on supersingular elliptic curves, error correction code-based encryption system, and lattice-based ring learning with errors. We performed a security comparison of Key Agreements protocols based on these three post-quantum cryptographic primitives and compared them with Discrete Logarithm Problem and Integer Factorization Problem. The comparison of security and its performance is presented by security level, the former by complexity analyses to achieve theoretical minimum key sizes, and the latter by simulation to assess a practical performance comparison. In the complexity analysis, as we increase the security level and then the size of the cryptographic keys increases, techniques based on isogeny outperform all other post-quantum algorithms in relation to key sizes at practical security level. In the performance comparison, the results show that the code-based protocol presents the best results among the others.