Fast Parallel DNA-Based Algorithms for Molecular Computation: Quadratic Congruence and Factoring Integers

• Published in: IEEE transactions on nanobioscience Vol. 11; no. 1; pp. 62 - 69
• Main Author: Chang, Weng-Long
• Format: Magazine Article
• Language: English
• Published: United States IEEE 01.03.2012; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adders; Algorithms; Biological cryptography; biological parallel computing; Computer Security; Computer Simulation; Computers, Molecular; Deoxyribonucleic acid; DNA; DNA - chemistry; DNA - genetics; DNA-based supercomputing; Electron tubes; Encoding; factoring integers; Libraries; Materials; Models, Genetic; molecular-based supercomputing; quadratic congruence; the RSA public-key cryptosystem; Zinc
• ISSN: 1536-1241; 1558-2639; 1558-2639
• DOI: 10.1109/TNB.2011.2167757

Assume that is a positive integer. If there is an integer such that , i.e., the congruence has a solution, then is said to be a quadratic congruence . If the congruence does not have a solution, then is said to be a quadratic noncongruence . The task of solving the problem is central to many important applications, the most obvious being cryptography. In this article, we describe a DNA-based algorithm for solving quadratic congruence and factoring integers. In additional to this novel contribution, we also show the utility of our encoding scheme, and of the algorithm's submodules. We demonstrate how a variety of arithmetic, shifted and comparative operations, namely bitwise and full addition, subtraction, left shifter and comparison perhaps are performed using strands of DNA.