基于DNA计算自组装模型的Diffie-Hellman算法破译(英文)  

Breaking the Diffie-Hellman Key Exchange Algorithm in the Tile Assembly Model

作　　者：陈智华[1] 

机构地区：[1]华中科技大学控制科学与工程系,武汉430074

出　　处：《计算机学报》2008年第12期2116-2122,共7页Chinese Journal of Computers

基　　金：国家自然科学基金(60803113,60533010,60674106);国家"八六三"高技术研究发展计划项目基金(2006AA012104)资助

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.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.

关 键 词：DNA计算 DNA自组装模型 离散对数 整数排序 PCR 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]