App. Res. of Comp. Accepted Paper
Vol. 43, 2026 No. 10

Design of FAST algebraic degree evaluation algorithm for trivium

Xu Qing1,2
Gao Bo3
Wan Jianxiong1,2
Li Leixiao1,2
Zhang Xiaodong1,2
1. College of Intelligent Science and Technology (College of Cyberspace Security), Inner Mongolia University of Technology, Hohhot InnerMongolia 010080, China
2. Inner Mongolia Key Laboratory of Beijang Cyberspace Security, Inner Mongolia Autonomous Region, Hohhot 010080, China
3. School of Information Engineering, Beijing Institute of Graphic Communication, Beijing 102600, China
DOI: 10.19734/j.issn.1001-3695.2025.12.0549

Abstract

Algebraic degree is a core metric for evaluating the security of cryptographic algorithms, as it directly determines their resistance to cryptanalytic techniques. However, existing algebraic-degree evaluation methods suffer from excessive computational cost and low efficiency. To address these challenges, this paper took the lightweight stream cipher Trivium as the research target and, from the perspective of monomial propagation, proposed a fast algebraic-degree evaluation framework for nonlinear feedback shift register type ciphers, termed FADEF. Building on a core monomial prediction technique, FADEF further improved the existing monomial-prediction-based evaluation pipeline and the intermediate-round variable substitution strategy, enabling fast and accurate estimation of the upper bound of the algebraic degree of Trivium's superpolynomial. Experimental results show that, compared with state-of-the-art monomial-prediction-based methods, FADEF achieves the same algebraic-degree upper bounds while reducing the runtime by approximately 50%. The proposed framework not only improves the efficiency of evaluating algebraic properties of lightweight ciphers, but also holds significant application value for future key-recovery attacks.

Foundation Support

国家自然科学基金资助项目(62062054)
内蒙古自然科学基金资助项目(2023MS06008,JY20250066)
内蒙古自治区重点研发和成果转化计划项目(2025KJHZ0039,2024SKYPT0012)
内蒙古自治区科技计划项目(2025YFHH0213)
内蒙古自治区高等学校青年科技人才发展项目(NJYT24035)
内蒙古自治区高等学校创新团队发展计划数据智能与安全(NMGIRT2506)
内蒙古自治区直属高校科研项目(JY20250065,JY20230019)
内蒙古自治区直属高校基本科研业务费项目(2025QN06026,JY20250065)
一流学科建设专项研究资助项目(YLXKZX-NGD-015)
内蒙古工业大学核心课程建设项目(YHX2024009)

Publish Information

DOI: 10.19734/j.issn.1001-3695.2025.12.0549
Publish at: Application Research of Computers Accepted Paper, Vol. 43, 2026 No. 10

Publish History

[2026-06-26] Accepted Paper

Cite This Article

徐卿, 高博, 万剑雄, 等. 面向Trivium的快速代数次数评价算法设计 [J]. 计算机应用研究, 2026, 43 (10). (2026-07-30). https://doi.org/10.19734/j.issn.1001-3695.2025.12.0549. (Xu Qing, Gao Bo, Wan Jianxiong, et al. Design of FAST algebraic degree evaluation algorithm for trivium [J]. Application Research of Computers, 2026, 43 (10). (2026-07-30). https://doi.org/10.19734/j.issn.1001-3695.2025.12.0549. )

About the Journal

  • Application Research of Computers Monthly Journal
  • Journal ID ISSN 1001-3695
    CN  51-1196/TP

Application Research of Computers, founded in 1984, is an academic journal of computing technology sponsored by Sichuan Institute of Computer Sciences under the Science and Technology Department of Sichuan Province.

Aiming at the urgently needed cutting-edge technology in this discipline, Application Research of Computers reflects the mainstream technology, hot technology and the latest development trend of computer application research at home and abroad in a timely manner. The main contents of the journal include high-level academic papers in this discipline, the latest scientific research results and major application results. The contents of the columns involve new theories of computer discipline, basic computer theory, algorithm theory research, algorithm design and analysis, blockchain technology, system software and software engineering technology, pattern recognition and artificial intelligence, architecture, advanced computing, parallel processing, database technology, computer network and communication technology, information security technology, computer image graphics and its latest hot application technology.

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