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混合整数线性规划是一种解决优化问题的常用方法.2012年,Mouha等人首次将该方法应用于密码算法的安全性评估,成功实现了对活跃S盒数下界的求解.PICO和RECTANGLE均为SPN型结构的轻量级分组密码算法,目前对于这两种算法的零相关线性分析研究尚待完善.本文首先针对PICO算法的零相关线性逼近问题,建立基于混合整数线性规划的模型并进行路径搜索,找到大量7轮PICO算法的零相关线性逼近,优于设计者给出的4轮零相关线性逼近.进一步地,通过构造7轮多维零相关线性区分器,对含白化密钥的10轮PICO算法进行密钥恢复攻击.该攻击能够恢复共50比特轮子密钥,其时间复杂度为2~(68.7)次10轮PICO加密,数据复杂度为2~(63.3)个已知明文,存储复杂度为2~(42.3)字节.最后,本文针对RECTANGLE算法的零相关线性逼近问题,采用类似方法进行搜索,同时借助算法本身的传播性质,找到了208条8轮RECTANGLE的零相关线性逼近,并给出了11轮RECTANGLE的零相关线性攻击.该攻击可恢复共44比特轮子密钥,其数据复杂度为2~(63)个已知明文,时间复杂度为2~(107)次11轮RECTANGLE加密运算.
Mixed integer linear programming is a common method to solve optimization problems. Mouha et al. First applied this method to the security evaluation of cryptographic algorithms in 2012, and succeeded in solving the lower bound of active S-boxes. Both PICO and RECTANGLE are SPN structure of the lightweight block cipher algorithm, the current zero-correlation linear analysis of these two algorithms remains to be improved.This paper first for the zero-correlation linear approximation of the PICO algorithm, the establishment of a model based on mixed integer linear programming and path Search and find a lot of 7-wheel PICO algorithm zero correlation linear approximation, better than the designer of the four zero-correlation linear approximation.Further, by constructing seven rounds of multi-dimensional zero-correlation linear discriminator, with the whitening key 10 rounds PICO algorithm for key recovery attack.The attack can recover a total of 50 bit wheel key, the time complexity is 2 ~ (68.7) 10 rounds of PICO encryption, the data complexity is 2 ~ (63.3) known plaintext, storage The complexity is 2 ~ (42.3) bytes.Finally, aiming at the zero-correlation linear approximation problem of RECTANGLE algorithm, this paper uses a similar method to search, and at the same time with the propagation nature of the algorithm itself, 208 208- TANGLE and gives eleven rounds of RECTANGLE zero-correlation linear attacks.The attack can recover a total of 44-bit wheel key, the data complexity is 2 ~ (63) known plaintext, the time complexity is 2 ~ (107) 11 rounds RECTANGLE encryption operation.