约减轮数分组密码LEA的差分分析

李艳俊; 李寅霜; 刘健; 王克

doi:10.11999/JEIT221282

约减轮数分组密码LEA的差分分析

doi: 10.11999/JEIT221282

李艳俊^{1, 2},
李寅霜^2, ,,
刘健¹,
王克²

1.
中国电子科技集团公司第十五研究所信息产业信息安全测评中心北京 100083
2.
北京电子科技学院北京 100070

基金项目: 北京高校“高精尖”学科建设项目(20210101Z0401)

详细信息

作者简介:
李艳俊：女，副教授，博士，研究方向为分组密码的设计与分析、密码协议设计与分析

李寅霜：女，硕士生，研究方向为分组密码分析方法

刘健：男，高级工程师，硕士，研究方向为网络与信息安全、商用密码应用安全性评估等

王克：男，讲师，博士，研究方向为公钥密码的设计与分析

通讯作者:
李寅霜　511228211@qq.com

中图分类号: TN918.1; TP309.2
计量
- 文章访问数: 307
- HTML全文浏览量: 228
- PDF下载量: 69
- 被引次数: 0
出版历程
- 收稿日期: 2022-10-10
- 修回日期: 2023-04-19
- 网络出版日期: 2023-04-24
- 刊出日期: 2023-10-31

Differential Analysis of Reduced Rounds Block Cipher LEA

LI Yanjun^{1, 2},
LI Yinshuang^{2
, ,},
LIU Jian¹,
WANG Ke²

1.
Information Industry Information Security Evaluation Center, The 15th Research Institute of China Electronics Technology Group Corporation, Beijing 100083, China
2.
Beijing Institute of Electronic Science and technology, Beijing 100070, China

Funds: The Advanced Discipline Construction Project of Beijing Universities (20210101Z0401)

摘要

摘要: LEA算法是面向软件的轻量级加密算法，在2019年成为 ISO/IEC 国际标准轻量级加密算法，具有快速加密、占用运算资源少等优点。该文基于多条输入输出差分相同的路径计算了差分概率，首次对LEA-128进行了13轮和14轮的密钥恢复攻击；采用提前抛弃技术，分别在12轮和13轮差分特征后面添加了1轮，恢复了96 bit密钥；其中13轮的密钥恢复攻击数据复杂度为2⁹⁸个明文，时间复杂度为2^86.7次13轮LEA-128解密；14轮的密钥恢复攻击数据复杂度为2¹¹⁸个明文，时间复杂度为2^110.6次14轮LEA-128解密。
- 轻量级分组密码 /
- ARX /
- 差分分析 /
- 密钥恢复攻击
Abstract: The LEA algorithm is a software-oriented lightweight encryption algorithm, which became the ISO/IEC international standard lightweight encryption algorithm in 2019. It has the advantages of fast encryption and less computing resources. The differential probability is calculated based on multiple paths with the same input-output difference, 13 and 14 rounds of key recovery attacks of LEA-128 are given for the first time. Using the early abort technology, one round is added after the 12-round and 13-round differential characteristic, and a total of 96 bit keys are recovered. The 13-round key recovery attack has a data complexity of 2⁹⁸ plaintext and a time complexity of 2^86.7 times of 13 rounds of LEA-128 decryption; the 14-round key recovery attack has a data complexity of 2¹¹⁸ plaintext and a time complexity of 2^110.6 times of 14 rounds of LEA-128 decryption.
- Lightweight block cipher /
- ARX /
- Differential analysis /
- Key recovery attack

HTML全文

图 1 LEA的轮变换

下载: 全尺寸图片幻灯片

图 2 存在的差分向量模式

下载: 全尺寸图片幻灯片

图 3 模加差分特性的线性不等式刻画

下载: 全尺寸图片幻灯片

图 4 13轮密钥恢复攻击

下载: 全尺寸图片幻灯片

图 5 14轮密钥恢复攻击

下载: 全尺寸图片幻灯片

表 1 LEA-128攻击分析结果比较

参考文献	攻击方法	区分器轮数	攻击轮数	时间复杂度	数据复杂度
[1]	差分分析	11	12	2⁸⁴	2¹⁰⁰
本文	差分分析	12/13	13/14	2^85.7/2^110.6	2⁹⁸/2¹¹⁸
[1]	不可能差分分析	10	12	–	–
[1]	零相关线性密码分析	7	9	–	–
[9]	零相关线性密码分析	9	9	2¹²⁷	2¹²⁷
[11]	零相关线性密码分析	10	–	–	–
[1]	积分分析	6	9	–	–
[12]	积分分析	7/8	–	–	2⁹⁶/2¹¹⁸
[13]	积分分析	8/9	10	2¹²⁰	2¹²⁴
[10]	积分分析	7	–	–	2⁹⁶
[1]	飞去来器分析方法	7	15	–	–
[14]	差分线性密码分析	12	–	–	–

下载: 导出CSV

算法1 最优特征的差分概率
输入：对于 r 轮密码的原始MILP模型。
输出：最优特征的概率多项式。
(1) 求解原始MILP模型并获得最优差分特征的概率 d 和　　 $(\varDelta _{ {\text{in} } }^ * ,\varDelta _{ {\text{out} } }^ * )$；
(2) 令 j = –1 ；
(3) 重复：
(4) 　j = j + 1 ;
(5) 　将原始MILP模型中的输入输出差分设为$(\varDelta _{ {\text{in} } }^ * ,\varDelta _{ {\text{out} } }^ * )$；
(6) 　令原始MILP模型中的目标函数 = d + j ；
(7) 　求解模型和不同特征的数量值$ {p_j} $；　(8) 直到${p_j}{2^{ - (d + j)} } \ge \displaystyle\sum\limits_{i = 0}^{j - 1} { {p_i}{2^{ - (d + i)} } }$；
(9) 令N = j – 1；
(10) 返回：概率多项式。

下载: 导出CSV

表 2 LEA算法的12轮差分特征及概率

轮数	$\Delta {X_0}$	$ \Delta {X_{\text{1}}} $	$\Delta {X_{\text{2}}}$	$\Delta {X_{\text{3}}}$	${\log _2}p$
0	C0000000	C0400080	40400010	40400012	–
1	80010000	8000000C	40000004	C0000000	–13
2	02001800	82000000	80000000	80010000	–8
3	00300100	00100000	00002000	02001800	–4
4	00020000	0001FF00	00400100	00300100	–15
5	00020000	00020000	00020000	00020000	–25
6	00000000	00000000	00000000	00020000	–5
7	00000000	00000000	00004000	00000000	–1
8	00000000	00000200	00000800	00000000	–2
9	00040000	00000030	00000100	00000000	–5
10	08002000	80000008	00000020	00040000	–7
11	00401110	C4000000	00008004	08002000	–8
12	80222188	22200400	81001400	00401110	–14

下载: 导出CSV

表 3 LEA算法的13轮差分特征及概率

轮数	$\Delta {X_0}$	$ \Delta {X_{\text{1}}} $	$\Delta {X_{\text{2}}}$	$\Delta {X_{\text{3}}}$	${\log _2}p$
0	C0000000	C0400080	40400010	40400012	–
1	80010000	8000000C	40000004	C0000000	–13
2	02001800	82000000	80000000	80010000	–8
3	00300100	00100000	00002000	02001800	–4
4	00020000	0001FF00	00400100	00300100	–15
5	00020000	00020000	00020000	00020000	–25
6	00000000	00000000	00000000	00020000	–5
7	00000000	00000000	00004000	00000000	–1
8	00000000	00000200	00000800	00000000	–2
9	00040000	00000030	00000100	00000000	–5
10	08002000	80000008	00000020	00040000	–7
11	00401110	C4000000	00008004	08002000	–8
12	80222188	22200400	81001400	00401110	–14
13	04491144	05190080	102800A1	80222088	–20

下载: 导出CSV

参考文献(22)

[1]	HONG D, LEE J K, KIM D C, et al. LEA: A 128-bit block cipher for fast encryption on common processors[C]. The 14th International Workshop on Information Security Applications, Jeju Island, Korea, 2013: 3–27.
[2]	BEAULIEU R, SHORS D, SMITH J, et al. The SIMON and SPECK lightweight block ciphers[C]. The 52nd Annual Design Automation Conference, San Francisco, USA, 2015: 175.
[3]	HONG D, SUNG J, HONG S, et al. HIGHT: A new block cipher suitable for low-resource device[C]. The 8th International Workshop on Cryptographic Hardware and Embedded Systems, Yokohama, Japan, 2006: 46–59.
[4]	GUO Ying, LI Lang, and LIU Botao. Shadow: A lightweight block cipher for IoT nodes[J]. IEEE Internet of Things Journal, 2021, 8(16): 13014–13023. doi: 10.1109/JIOT.2021.3064203
[5]	KANG Man, LI Yongqiang, JIAO Lin, et al. Differential analysis of ARX block ciphers based on an improved genetic algorithm[J]. Chinese Journal of Electronics, 2023, 32(2): 225–236. doi: 10.23919/cje.2021.00.415
[6]	AZIMI S A, RANEA A, SALMASIZADEH M, et al. A bit-vector differential model for the modular addition by a constant and its applications to differential and impossible-differential cryptanalysis[J]. Designs, Codes and Cryptography, 2022, 90(8): 1797–1855. doi: 10.1007/s10623-022-01074-8
[7]	COUTINHO M and SOUZA NETO T C. Improved linear approximations to ARX ciphers and attacks against ChaCha[C]. The 40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, 2021: 711–740.
[8]	WANG Feifan and WANG Gaoli. Improved differential-linear attack with application to round-reduced Speck32/64[C]. The 20th International Conference on Applied Cryptography and Network Security, Rome, Italy, 2022: 792–808.
[9]	ZHANG Kai, GUAN Jie, and HU Bin. Zero correlation linear cryptanalysis on LEA family ciphers[J]. Journal of Communications, 2016, 11(7): 677–685. doi: 10.12720/jcm.11.7.677-685
[10]	SUN Ling, WANG Wei, LIU Ru, et al. MILP-aided bit-based division property for ARX ciphers[J]. Science China Information Sciences, 2018, 61(11): 118102. doi: 10.1007/s11432-017-9321-7
[11]	崔婷婷. 分组密码算法和流密码算法的安全性分析[D]. [博士论文], 山东大学, 2018. CUI Tingting. Security analysis of block ciphers and stream ciphers[D]. [Ph. D. dissertation], Shandong University, 2018.
[12]	孙玲. 分组密码攻击模型的构建和自动化密码分析[D]. [博士论文], 山东大学, 2019. SUN Ling. The construction of attack model for block ciphers and automatic cryptanalysis[D]. [Ph. D. dissertation], Shandong University, 2019.
[13]	李航, 任炯炯, 陈少真. 减轮LEA密码算法的积分攻击[J]. 电子学报, 2020, 48(1): 17–27. doi: 10.3969/j.issn.0372-2112.2020.01.003 LI Hang, REN Jiongjiong, and CHEN Shaozhen. Integral attack on reduced-round LEA cipher[J]. Acta Electronica Sinica, 2020, 48(1): 17–27. doi: 10.3969/j.issn.0372-2112.2020.01.003
[14]	刘晟源. 基于MILP对WARP、GOST2和LEA算法的密码分析[D]. [硕士论文], 华东师范大学, 2022. LIU Shengyuan. Cryptanalysis of WARP, GOST2 and LEA algorithms based on MILP[D]. [Master dissertation], East China Normal University, 2022.
[15]	MOUHA N, WANG Qingju, GU Dawu, et al. Differential and linear cryptanalysis using mixed-integer linear programming[C]. The 7th International Conference on Information Security and Cryptology, Beijing, China, 2011: 57–76.
[16]	WU Shengbao and WANG Mingsheng. Security evaluation against differential cryptanalysis for block cipher structures[R]. Paper 2011/551, 2011.
[17]	SUN Siwei, HU Lei, WANG Peng, et al. Automatic security evaluation and (related-key) differential characteristic search: Application to SIMON, PRESENT, LBlock, DES(L) and other bit-oriented block ciphers[C]. The 20th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, China, 2014: 158–178.
[18]	SUN Siwei, HU Lei, WANG Meiqin, et al. Towards finding the best characteristics of some bit-oriented block ciphers and automatic enumeration of (related-key) differential and linear characteristics with predefined properties[R]. Paper 2014/747, 2014: 747.
[19]	LIPMAA H and MORIAI S. Efficient algorithms for computing differential properties of addition[C]. The 8th International Workshop on Fast Software Encryption, Yokohama, Japan, 2001: 336–350.
[20]	FU Kai, WANG Meiqin, GUO Yinghua, et al. MILP-based automatic search algorithms for differential and linear trails for speck[C]. The 23rd International Conference on Fast Software Encryption, Bochum, Germany, 2016: 268–288.
[21]	LAI Xuejia, MASSEY J L, and MURPHY S. Markov ciphers and differential cryptanalysis[C]. 1991 Workshop on the Theory and Application of Cryptographic Techniques, Brighton, UK, 1991: 17–38.
[22]	BAGHERZADEH E and AHMADIAN Z. MILP‐based automatic differential search for LEA and HIGHT block ciphers[J]. IET Information Security, 2020, 14(5): 595–603. doi: 10.1049/iet-ifs.2018.5539