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中文摘要：
DNA自组装计算模型是近年来引人关注的计算模型，已有基于自组装模型的二进制加法、乘法以及有限域中的加法和乘法的讨论．文中利用DNA自组装模型设计的模乘系统，实现了素数P的本原根g连续乘方后模p的数的排列，从而可以在线性时间内求解离散对数，为破译Diffie—Hellman密钥交换算法提供了新的生物方法．该模乘系统使用了Θ（p）种自组装类型，组装的时间复杂度为Θ（p-1）．系统最后组装结果提取出报告链后，经过PCR和凝胶电泳读取离散对数结果．该模型扩展了DNA自组装计算模型的应用，为求取离散对数提供了新思路．
英文摘要：
Recent experiments have demonstrated that the simple binary arithmetic and logical operations can be computed by the self-assembly DNA tiles. This paper shows how the tile assembly process can be used to break Diffie-Hellman key exchange. In order to achieve this, the author used tile systems to construct the integers permutation from 1 to p-1 based on the truth table of the following numbers modular p： g mod p, g2 rood p,…,g^p-1 rood p. The output of the systems can be read by the standard sequence-reading operation that uses a combination of PCR and gel electrophoresis. Through the processes of tile systems, we can pick out the discrete logarithm result which is the secret key in the Diffie-Hellman algorithm. So the key exchange by Diffie-Hellman algorithm is unsafe. The system can be carried out in Θ（p-1） assembly time with Θ（p） tiles. The methods extend the applications of self-assembly model.
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