Linear Analysis of Lightweight Cipher ACE and SPIX Based on Mixed-Integer Linear Programming

LIU Shuai; REN Xiao-guang; WANG Shi-xiong; GUAN Jie; ZHANG Xiao-chuan; TAN Jie; WANG Jun

doi:10.12263/DZXB.20230673

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Linear Analysis of Lightweight Cipher ACE and SPIX Based on Mixed-Integer Linear Programming

PAPERS | 更新时间：2025-12-08

- Linear Analysis of Lightweight Cipher ACE and SPIX Based on Mixed-Integer Linear Programming
- ACTA ELECTRONICA SINICA Vol. 52, Issue 9, Pages: 3065-3074(2024)
- 作者机构：
  
  1.智能博弈与决策实验室，北京 100091
  2.军事科学院，北京 100091
  3.战略支援部队信息工程大学密码工程学院，河南郑州 450001
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(62102440)
- DOI：10.12263/DZXB.20230673
  CLC： TN918.1
- Received：14 July 2023，
  
  Revised：2024-04-09，
  
  Published：25 September 2024
- 稿件说明：
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刘帅, 任小广, 王世雄, 等. 基于MILP的轻量级密码算法ACE与SPIX的线性分析[J]. 电子学报, 2024, 52(09): 3065-3074.

LIU Shuai, REN Xiao-guang, WANG Shi-xiong, et al. Linear Analysis of Lightweight Cipher ACE and SPIX Based on Mixed-Integer Linear Programming[J]. Acta Electronica Sinica, 2024, 52(09): 3065-3074.
刘帅, 任小广, 王世雄, 等. 基于MILP的轻量级密码算法ACE与SPIX的线性分析[J]. 电子学报, 2024, 52(09): 3065-3074. DOI：10.12263/DZXB.20230673

LIU Shuai, REN Xiao-guang, WANG Shi-xiong, et al. Linear Analysis of Lightweight Cipher ACE and SPIX Based on Mixed-Integer Linear Programming[J]. Acta Electronica Sinica, 2024, 52(09): 3065-3074. DOI：10.12263/DZXB.20230673

摘要

研究了轻量级密码算法ACE与SPIX的线性性质.给出了环型与门组合结构精确的混合整数线性规划下的线性性质刻画，并将算法ACE与SPIX的非线性操作转化为环型与门组合.基于此构建了ACE置换与SLISCP置换的混合整数线性规划下的线性模型，求解模型得到了2至4步ACE置换与2至5步SLISCP置换最优的线性迹.证明了7步、12步ACE置换分别达到了128比特与320比特的安全目标，7步、13步SLISCP置换分别达到了128比特与256比特的安全目标.对于任意步数的ACE置换与SLISCP置换，认证加密算法ACE-AE-128与SPIX均能够抵抗明文处理阶段的线性区分攻击.

Abstract

The linear property of lightweight cipher ACE and SPIX was researched. The linear property of ring AND-gate combination was described accurately with mixed-integer linear programming. The nonlinear operation of ACE and SPIX was transformed into ring AND-gate combination. Based on this

the linear models of ACE permutation and SLISCP permutation were constructed with mixed-integer linear programming. The models returned the optimal linear characteristics of 2-step to 4-step ACE permutation and 2-step to 5-step SLISCP permutation. It was proved that 7-step and 12-step ACE permutation achieved the 128-bit security and 320-bit security respectively

and 7-step and 13-step SLISCP permutation achieved the 128-bit security and 256-bit security respectively. For the ACE permutation and SLISCP permutation with any number of steps

authenticated encryption algorithm ACE-AE-128 and SPIX can resist the linear distinguish attack of plaintext processing stage.

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references

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