Abstract
The RSA public-key cryptosystem is an algorithm that converts a plain-text to its corresponding cipher-text, and then converts the cipher-text back into its corresponding plain-text. In this article, we propose five DNA-based algorithms—parallel adder, parallel subtractor, parallel multiplier, parallel comparator, and parallel modular arithmetic—that construct molecular solutions for any (plain-text, cipher-text) pair for the RSA public-key cryptosystem. Furthermore, we demonstrate that an eavesdropper can decode an encrypted message overheard with the linear steps in the size of the encrypted message overheard.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Rivest RL, Shamir A, Adleman L (1978) A method for obtaining digital signatures and public-key crytosystem. Commun ACM 21:120–126
Feynman RP (1961) There’s plenty of room at the bottom. In: Gilbert DH (ed) Minaturization. Reinhold, New York, pp 282–296
Adleman L (1994) Molecular computation of solutions to combinatorial problems. Science 266:1021–1024
Lipton RJ (1995) DNA solution of hard computational problems. Science 268:542–545
Quyang Q, Kaplan PD, Liu S, Libchaber A (1997) DNA solution of the maximal clique problem. Science 278:446–449
Amos M (1997) DNA computation. PhD thesis, Department of Computer Science, the University of Warwick
Harju T, Li C, Petre I, Rozenberg G (2005) Parallelism in gene assembly. In: DNA computing. Lecture notes in computer science, vol 3384, p 686. doi:10.1007/11493785_12
Thachuk C, Manuch J, Rafiey A, Mathieson L-A, Stacho L, Condon A (2010) An algorithm for the energy barrier problem without pseudoknots and temporary arcs. Pac Symp Biocomput 15:108–119
Zadeh JN, Wolfe BR, Pierce NA (2010) Nucleic acid sequence design via efficient ensemble defect optimization. J Comput Chem. doi:10.1002/jcc.21633
Xiao D, Li W, Zhang Z, He L (2005) Solving the maximum cut problems in the Adleman–Lipton model. Biosystems 82:203–207
Yeh C-W, Chu C-P, Wu K-R (2006) Molecular solutions to the binary integer programming problem based on DNA computation. Biosystems 83(1):56–66
Zhang DY, Turberfield AJ, Yurke B, Winfree E (2007) Engineering entropy-driven reactions and networks catalyzed by DNA. Science 318(5853):1121–1125
Boneh D, Dunworth C, Lipton RJ (1996) Breaking DES using a molecular computer. In: Proceedings of the 1st DIMACS workshop on DNA based computers, 1995. DIMACS series in discrete mathematics and theoretical computer science, vol 27. American Mathematical Society, Providence, pp 37–66
Adleman L, Rothemund PWK, Roweis S, Winfree E (1999) On applying molecular computation to the data encryption standard. In: The 2nd annual workshop on DNA computing, Princeton University. DIMACS series in discrete mathematics and theoretical computer science. American Mathematical Society, Providence, pp 31–44
Zhang DY, Seelig G (2011) DNA-based fixed gain amplifiers and linear classifier circuits. In: DNA 16. Lecture notes in computer science, vol 6518, p 176
Yeh C-W, Chu C-P (2008) Molecular verification of rule-based systems based on DNA computation. IEEE Trans Knowl Data Eng 20(7):965–975
Guarnieri F, Fliss M, Bancroft C (1996) Making DNA add. Science 273:220–223
Ho M(S-H) (2005) Fast parallel molecular solutions for DNA-based supercomputing: the subset-product problem. Biosystems 80:233–250
Ahrabian H, Nowzari-Dalini A (2004) DNA simulation of nand Boolean circuits. Adv Model Optim 6(2):33–41
Schuster A (2005) DNA databases. Biosystems 81:234–246
Paun G, Rozenberg G, Salomaa A (1998) DNA computing: new computing paradigms. Springer, New York. ISBN:3-540-64196-3
Boneh D, Dunworth C, Lipton RJ, Sgall J (1996) On the computational power of DNA. Discrete Appl Math 71:79–94. Special Issue on Computational Molecular Biology
Amos M (2005) Theoretical and experimental DNA computation. Springer, Berlin
Braich RS, Johnson C, Rothemund PWK, Hwang D, Chelyapov N, Adleman LM Solution of a satisfiability problem on a gel-based DNA computer. In: Proceedings of the 6th international conference on DNA computation. Lecture notes in computer science. Springer, Berlin
Braich RS, Johnson C, Rothemund PWK, Hwang D, Chelyapov N, Adleman LM (2002) Solution of a 20-variable 3-SAT problem on a DNA computer. Science 296(5567):499–502
Diffie W, Hellman M (1976) New directions in cryptography. IEEE Trans Inf Theory IT-22(6):644–654
Shor PW (1997) Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J Comput 26(5):1484–1509
Chang W-L, Ho M, Guo M (2005) Fast parallel molecular algorithms for DNA-based computation: factoring integers. IEEE Trans Nanobiosci 4(2):149–163
Li K, Zou S, Xv J (2008) Fast parallel molecular algorithms for DNA-based computation: solving the elliptic curve discrete logarithm problem over GF(2n). J Biomed Biotechnol 2008:518093. doi:10.1155/2008/518093
Chang W-L, Huang S-C, Lin KW, Ho M(SH) (2009) Fast parallel DNA-based algorithms for molecular computation: discrete logarithm. J Supercomput
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chang, WL., Lin, K.W., Chen, JC. et al. Molecular solutions of the RSA public-key cryptosystem on a DNA-based computer. J Supercomput 61, 642–672 (2012). https://doi.org/10.1007/s11227-011-0627-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11227-011-0627-z