基于纠错码的SM3改进算法

目前密码分析者已经可以在较短的时间内有效找到MD5、SHA1等国际密码杂凑算法的碰撞，通过熵增来增强杂凑值的随机性是提高密码杂凑算法抗碰撞性的有效途径，因此提出一种将纠错码和SM3算法迭代结构融合的改进方案。首先，基于纠错码的线性性质和最小汉明距离最大化原则，选择拟阵理论所构建的二进制线性分组码，计算出其系统形式的生成矩阵，并通过循环移位来消除比特之间的规律，并计算最终产生的有效码字；其次，在线性分组码中遵循周期性原则选取最优码字来构建初始常量值，并将其赋值于初始寄存器中，同时在迭代结构中引入初始寄存器构成算法的压缩函数，完成杂凑算法迭代结构的二次构建；最后，考虑杂凑值信息熵对算法混乱度的评估能力，将提出的方案和2种现有公开的国际密码杂凑算法进行对比实验，同时进行算法效率、内存损耗以及雪崩效应测试并进行综合评价。实验结果表明，本文方案在不改变运算效率的前提下具有稳定的雪崩效应，运行过程中的内存损耗相比SM3算法降低0.01~0.07MB，同时杂凑值的信息熵值高于其他两类对比算法。表明提出的基于纠错码的改进方案能够通过熵增证明杂凑值比特之间的随机性更高，更好实现隐藏明文和杂凑值之间统计信息的目的，提高了密码杂凑算法的安全性。

Improved SM3 Algorithm Based on Error-correcting Code

Cryptanalysts now can effectively find the collisions of MD5, SHA1 and other international hash algorithms in a short time, increasing entropy to enhance the randomness of hash value is an effective way to improve the anti-collision performance of hash algorithm, Therefore, an improved scheme combining the iterative structure of error-correcting code and SM3 algorithm was proposed. Firstly, based on the linear properties of error-correcting codes and the maximization principle of minimum Hamming distance, the binary linear block codes constructed by matroid theory were selected to calculate their systematic form of generation matrix, the rules between bits were eliminated by cyclic shift, and the effective code words were calculated. Secondly, in the linear block code, the optimal code word was selected to construct the initial constant value according to the periodicity principle, and the value was assigned to the initial register. At the same time, the compression function of the initial register formation algorithm was introduced into the iterative structure to complete the second construction of the iterative structure of the hash algorithm. Finally, considering the evaluation ability of hash value information entropy on algorithm chaos degree, the proposed scheme was compared with two existing international hash algorithms, and the algorithm efficiency, memory loss and avalanche effect were tested and comprehensively evaluated. Experimental results showed that the proposed scheme had stable avalanche effect without changing the computational efficiency, the memory loss during operation was 0.01~0.07MB lower than that of SM3 algorithm, and the information entropy of the hash value was higher than that of other two comparison algorithms. It showed that the proposed scheme based on error-correcting code can proved by entropy bits hash value between the randomness of the higher, better to achieve the purpose of hiding statistics between plaintext and hash value, and improved the security of hash algorithm.