Analysis of methods and algorithms for generating key data for FALCON-like electronic signature algorithms

IF 0.2 Q4 ENGINEERING, ELECTRICAL & ELECTRONIC Visnyk NTUU KPI Seriia-Radiotekhnika Radioaparatobuduvannia Pub Date : 2022-06-24 DOI:10.30837/rt.2022.2.209.08
O. Kachko, M. Yesina, K.O. Kuznetsova
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Abstract

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.
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falcon类电子签名算法关键数据生成方法与算法分析
目前和将来,标准化的非对称密码转换(如电子签名(ES))的数学方法、机制和算法已经并将用于信息密码保护。电子签名是网络安全的重要组成部分,可以提供所处理信息和数据的完整性、不可抗拒性和真实性等优质信息安全服务。然而,有充分的理由怀疑,在后量子时期,现有的ES标准将被打破和破坏,使用经典和量子密码分析系统与适当的数学,软件和硬件软件。一项分析证实,量子计算机已经被开发、制造和使用。本文主要研究了电子签名类猎鹰算法中关键数据的生成方法和算法。考虑了满足高斯分布的隼形电子签名算法的一些基本算法,即密钥数据生成算法和随机多项式f, g生成算法。Falcon算法本身由于公钥值和签名长度令人满意,成为后量子电子签名大赛的决赛选手,但密钥数据生成算法使用的方法多,实现难度大。Falcon的作者对多项式n=512, 1024使用这种算法。为了提高第六级密码稳定性,可以将该算法扩展到n=2048。本文主要研究Falcon算法,考虑到其在生成关键数据时n=512, 1024, 2048的扩展。此外,本文还考虑了证明选择一种数学装置来实现软件包的结果,该软件包用于生成用于电子签名的加密算法的密钥对,以便创建可靠的电子签名。
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Visnyk NTUU KPI Seriia-Radiotekhnika Radioaparatobuduvannia
Visnyk NTUU KPI Seriia-Radiotekhnika Radioaparatobuduvannia ENGINEERING, ELECTRICAL & ELECTRONIC-
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