Fast Parallel Molecular Algorithms for DNA-Based Computation: Solving the Elliptic Curve Discrete Logarithm Problem over GF(2n)

• Published in: BioMed research international Vol. 2008; no. 2008; pp. 1 - 10
• Main Authors: Li, Kenli, Xv, Jin, Zou, Shuting
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2008; John Wiley & Sons, Inc; Hindawi Limited
• Subjects: Algorithms; Biomedical research; Curves, Elliptic; Deoxyribonucleic acid; Digital signatures; DNA; Ellipse; Embedded systems; Genetic algorithms; Molecular dynamics; Network security; Properties; China
• ISSN: 2314-6133; 1110-7243; 2314-6141; 2314-6141; 1110-7251
• DOI: 10.1155/2008/518093

Elliptic curve cryptographic algorithms convert input data to unrecognizable encryption and the unrecognizable data back again into its original decrypted form. The security of this form of encryption hinges on the enormous difficulty that is required to solve the elliptic curve discrete logarithm problem (ECDLP), especially over GF(2n), n∈Z+. This paper describes an effective method to find solutions to the ECDLP by means of a molecular computer. We propose that this research accomplishment would represent a breakthrough for applied biological computation and this paper demonstrates that in principle this is possible. Three DNA-based algorithms: a parallel adder, a parallel multiplier, and a parallel inverse over GF(2n) are described. The biological operation time of all of these algorithms is polynomial with respect to n. Considering this analysis, cryptography using a public key might be less secure. In this respect, a principal contribution of this paper is to provide enhanced evidence of the potential of molecular computing to tackle such ambitious computations.