Fast parallel molecular algorithms for DNA-based computation: factoring integers

• Published in: IEEE transactions on nanobioscience Vol. 4; no. 2; pp. 149 - 163
• Main Authors: Weng-Long Chang, Minyi Guo, Ho, M.S.-H.
• Format: Magazine Article
• Language: English
• Published: United States IEEE 01.06.2005; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Biological parallel computing; Biology computing; Computer errors; Computer Security; Computers, Molecular; Computing Methodologies; Concurrent computing; Data mining; Data security; DNA - chemistry; DNA - genetics; DNA computing; DNA-based algorithms; DNA-based computing; factoring integers; Information Storage and Retrieval - methods; Numerical Analysis, Computer-Assisted; Parallel processing; Public key; Public key cryptography; RSA public-key cryptosystem; Sequence Analysis, DNA - methods; Signal Processing, Computer-Assisted; Testing
• ISSN: 1536-1241; 1558-2639
• DOI: 10.1109/TNB.2005.850474

The RSA public-key cryptosystem is an algorithm that converts input data to an unrecognizable encryption and converts the unrecognizable data back into its original decryption form. The security of the RSA public-key cryptosystem is based on the difficulty of factoring the product of two large prime numbers. This paper demonstrates to factor the product of two large prime numbers, and is a breakthrough in basic biological operations using a molecular computer. In order to achieve this, we propose three DNA-based algorithms for parallel subtractor, parallel comparator, and parallel modular arithmetic that formally verify our designed molecular solutions for factoring the product of two large prime numbers. Furthermore, this work indicates that the cryptosystems using public-key are perhaps insecure and also presents clear evidence of the ability of molecular computing to perform complicated mathematical operations.