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自Diffie、Hellman提出公钥密码体制以来,公钥加密算法设计和分析技巧在突飞猛进地发展。然而需要引起我们注意的是很大部分公钥密码体制基于离散对数,这些密码算法的有效性依赖于计算离散对数的难度,本文从理论分析的角度看离散对数问题的比特安全性,借助二叉树遍历,递归反证的思想,由离散对数问题的困难性证得求解离散对数高位比特的困难性。
Since Diffie and Hellman proposed the public key cryptosystem, the design and analysis skills of public key cryptosystems have been developing by leaps and bounds. However, what we need to pay attention to is that most of public-key cryptosystems are based on discrete logarithms. The effectiveness of these cryptographic algorithms depends on the difficulty of computing discrete logarithms. In this paper, we study the bit-safety of discrete logarithms problem from the perspective of theoretical analysis, With the idea of binary tree traversal and recursive anti-carding, the difficulty of solving the discrete high-order bits of logarithm by the difficult card of discrete logarithm problem.