Analysis of methods and algorithms for generating key data for FALCON-like electronic signature algorithms
DOI:
https://doi.org/10.30837/rt.2022.2.209.08Keywords:
post-quantum cryptography, electronic signature algorithm, lattice theory, Falcon algorithm, key pair generationAbstract
At present and in the future, mathematical methods, mechanisms and algorithms of standardized asymmetric cryptotransformations such as electronic signature (ES) are and will be used for information cryptographic protection. Electronic signature is the main and essential component of cybersecurity, in terms of providing quality information security services such as integrity, irresistibility and authenticity of information and data being processed. However, there are well-founded suspicions that in the post-quantum period the existing ES standards will be broken and compromised using classical and quantum cryptanalytic systems with appropriate mathematical, software and hardware-software. An analysis was performed, which confirms that quantum computers have already been developed, manufactured and used. This work is devoted to the analysis of methods and algorithms for generating key data for Falcon-like algorithms of electronic signature. Some of the basic algorithms for Falcon-shaped algorithms of electronic signature are considered, namely the algorithm of key data generation and algorithm of random polynomials f, g generation, which satisfy the Gauss distribution. The Falcon algorithm itself is the finalist of the post-quantum electronic signature contest due to the satisfactory value of the public key and signature lengths, but the key data generation algorithm uses many methods and difficult to implement. The Falcon authors use this algorithm for polynomials n=512, 1024. To increase the sixth level of cryptostability, this algorithm can be expanded for n=2048. This work is devoted to study the Falcon algorithm, taking into account its expansion for n=512, 1024, 2048 in terms of generating key data. Also, the paper considers the results of justifying the choice of a mathematical apparatus for implementing a software package for generating a key pair of a cryptographic algorithm for an electronic signature in order to create reliable electronic signatures.
References
Post-Quantum Cryptography. Round 3 Submissions. [Електронний ресурс]. Режим доступу: https://csrc.nist.gov/Projects/post-quantum-cryptography/round-3-submissions.
Falcon: Fast-Fourier Lattice-based Compact Signatures over NTRU. [Електронний ресурс]. Режим доступу: https://falcon-sign.info/.
Donald E. Knuth The Art of Computer Programming. Seminumerical algorithms. Vol. 2 (3rd ed.). Boston: Addison–Wesley, 1998. 774p.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).