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Journal of Biomedicine and Biotechnology
Volume 2008 (2008), Article ID 518093, 10 pages
Research Article

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

1Embedded System and Networking Laboratory, College of Computer and Communication, Hunan University, Changsha 410082, China
2Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Received 16 July 2007; Accepted 25 January 2008

Academic Editor: Daniel Howard

Copyright Β© 2008 Kenli Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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), π‘›βˆˆπ‘+. 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.