Aspects of Molecular Computing pp 167-188 | Cite as
DNA-based Cryptography
Abstract
Recent research has considered DNA as a medium for ultra-scale computation and for ultra-compact information storage. One potential key application is DNA-based, molecular cryptography systems. We present some procedures for DNA-based cryptography based on one-time-pads that are in principle unbreakable. Practical applications of cryptographic systems based on one-time-pads are limited in conventional electronic media by the size of the one-time-pad; however DNA provides a much more compact storage medium, and an extremely small amount of DNA suffices even for huge one-time-pads. We detail procedures for two DNA one-time-pad encryption schemes: (i) a substitution method using libraries of distinct pads, each of which defines a specific, randomly generated, pair-wise mapping; and (ii) an XOR scheme utilizing molecular computation and indexed, random key strings. These methods can be applied either for the encryption of natural DNA or for artificial DNA encoding binary data. In the latter case, we also present a novel use of chip-based DNA micro-array technology for 2D data input and output. Finally, we examine a class of DNA steganography systems, which secretly tag the input DNA and then hide it within collections of other DNA. We consider potential limitations of these steganographic techniques, proving that in theory the message hidden with such a method can be recovered by an adversary. We also discuss various modified DNA steganography methods which appear to have improved security.
Keywords
Compression Ratio Discrete Math Encrypt Message Theoretical Comp DIMACS SeriesPreview
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References
- 1.Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)CrossRefGoogle Scholar
- 2.Barnes, W.M.: PCR amplification of up to 35-kb DNA with high fidelity and high yield from bacteriophage templates. Proc. Natl. Acad. Sci. 91, 2216–2220 (1994)CrossRefGoogle Scholar
- 3.Baum, E.B.: Building an associative memory vastly larger than the brain. Science 268, 583–585 (1995)CrossRefGoogle Scholar
- 4.Bell, T., Witten, I.H., Cleary, J.G.: Modeling for Text Compression. ACM Computing Surveys 21(4), 557–592 (1989)CrossRefGoogle Scholar
- 5.Boneh, D., Dunworth, C., Lipton, R.J.: Breaking DES Using a Molecular Computer. In: Baum, E.B., Lipton, R.J. (eds.) DNA Based Computers. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, Providence (1996)Google Scholar
- 6.Blanchard, A.P., Kaiser, R.J.: High-density oligonucleotide arrays. Biosens. Bioelec. 11, 687–690 (1996)CrossRefGoogle Scholar
- 7.Boneh, D., Dunworth, C., Lipton, R.J., Sgall, J.: Making DNA computers error resistant. In: Landwaber, L., Baum, E. (eds.) DNA based computer II. DIMACS series in Discrete Math. and Theoretical Comp. Sci, vol. 44 (1999)Google Scholar
- 8.Chee, M., Yang, R., Hubbell, E., Berno, A., Huang, X.C., Stern, D., Winkler, J., Lockhart, D.J., Morris, M.S., Fodor, S.P.A.: Accessing genetic information with high-density DNA arrays. Science 274, 610–614 (1996)CrossRefGoogle Scholar
- 9.Cover, T.M., Thomas, J.A.: Elements of Information Theory. John Wiley & Sons, New York (1991)zbMATHCrossRefGoogle Scholar
- 10.Deaton, R., Murphy, R.C., Garzon, M., Franceschetti, D.R., Stevens Jr., S.E.: Good Encodings for DNA-based Solutions to Combinatorial Problems. In: Landwaber, L., Baum, E. (eds.) DNA based computer II. DIMACS series in Discrete Math. and Theoretical Comp. Sci, vol. 44 (1999); Proceedings of the Second Annual Meeting on DNA Based Computers. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, pp. 1052–1798. American Mathematical Society, Providence (1996)Google Scholar
- 11.Deaton, R., Murphy, R.C., Garzon, M., Franceschetti, D.R., Stevens Jr., S.E.: Reliability and efficiency of a DNA-based computation. Phys. Rev. Lett. 80, 417–420 (1998)CrossRefGoogle Scholar
- 12.Fodor, S., Read, J.L., Pirrung, M.C., Stryer, L., Tsai Lu, A., Solas, D.: Lightdirected spatially addressable parallel chemical synthesis. Science 251, 767–773 (1991)CrossRefGoogle Scholar
- 13.Frutos, A.G., Thiel, A.J., Condon, A.E., Smith, L.M., Corn, R.M.: DNA Computing at Surfaces: 4 Base Mismatch Word Design. In: Rubin, H., Wood, D. (eds.) DNA based computer III. DIMACS series in Discrete Math. and Theoretical Comp. Sci, vol. 48, p. 238 (1999)Google Scholar
- 14.Gray, J.M., Frutos, T.G., Michael Berman, A., Condon, A.E., Lagally, M.G., Smith, L.M., Corn, R.M.: Reducing Errors in DNA Computing by Appropriate Word Design (November 1996)Google Scholar
- 15.Grumbach, S., Tahi, F.: A new challenge for compression algorithms: genetic sequences. Inf. Proc. and Management 30(6), 875–886 (1994)zbMATHCrossRefGoogle Scholar
- 16.Guarnieri, F., Fliss, M., Bancroft, C.: Making DNA Add. Science 273, 220–223 (1996)CrossRefGoogle Scholar
- 17.Gupta, V., Parthasarathy, S., Zaki, M.J.: Arithmetic and Logic Operations with DNA. In: Rubin, H., Wood, D. (eds.) DNA based computer III. DIMACS series in Discrete Math. and Theoretical Comp. Sci, vol. 48, pp. 212–220 (1999)Google Scholar
- 18.Hagiya, M., Arita, M., Kiga, D., Sakamoto, K., Yokoyama, S.: Towards Parallel Evaluation and Learning of Boolean μ-Formulas with Molecules. In: Rubin, H., Wood, D. (eds.) DNA based computer III. DIMACS series in Discrete Math. and Theoretical Comp. Sci., vol. 48, pp. 105–114 (1999)Google Scholar
- 19.Head, T.: Splicing schemes and DNA. In: Rozenberg, G., Salomaa, A. (eds.) Lindenmayer Systems; Impact on Theoretical computer science and developmental biology, pp. 371–383. Springer, Berlin (1992)Google Scholar
- 20.Henikoff, S., Henikoff, J.G.: Amino acid substitution matrices from protein blocks. Proc. Natl. Acad. Sci. 89, 10915–10919 (1992)CrossRefGoogle Scholar
- 21.Kahn, D.: The Codebreakers. Macmillan, New York (1967)Google Scholar
- 22.Klein, J.P., Leete, T.H., Rubin, H.: A biomolecular implementation of logical reversible computation with minimal energy dissipation. In: Kari, L., Rubin, H., Wood, D.H. (eds.) Proceedings 4th DIMACS Workshop on DNA Based Computers, pp. 15–23. University of Pennysylvania, Philadelphia (1998)Google Scholar
- 23.Kotera, M., Bourdat, A.G., Defrancq, E., Lhomme, J.: A highly efficient synthesis of oligodeoxyribonucleotides containing the 2’-deoxyribonolactone lesion. J. Am. Chem. Soc. 120, 11810–11811 (1998)CrossRefGoogle Scholar
- 24.LaBean, T.H., Butt, T.R.: Methods and materials for producing gene libraries, U.S. Patent Number 5,656,467 (1997)Google Scholar
- 25.LaBean, T., Kauffman, S.A.: Design of synthetic gene libraries encoding random sequence proteins with desired ensemble characteristics. Protein Science 2, 1249–1254 (1993)CrossRefGoogle Scholar
- 26.LaBean, T.H., Winfree, E., Reif, J.H.: Experimental Progress in Computation by Self-Assembly of DNA Tilings. DNA Based Computers V (1999)Google Scholar
- 27.LaBean, T.H., Yan, H., Kopatsch, J., Liu, F., Winfree, E., Reif, H.J.: The construction, analysis, ligation and self-assembly of DNA triple crossover complexes. J. Am. Chem. Soc. 122, 1848–1860 (2000)CrossRefGoogle Scholar
- 28.Li, X., Yang, X., Qi, J., Seeman, N.C.: Antiparallel DNA double crossover molecules as components for nanoconstruction. J. Amer. Chem. Soc. 118, 6131–6140 (1996)CrossRefGoogle Scholar
- 29.Loewenstern, Y.: Significantly Lower Entropy Estimates for Natural DNA Sequences. In: DCC: Data Compression Conference, pp. 151–161. IEEE Computer Society TCC, Los Alamitos (1997)CrossRefGoogle Scholar
- 30.Mao, C., LaBean, T.H., Reif, J.H., Seeman, N.C.: Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature 407, 493–496 (2000)CrossRefGoogle Scholar
- 31.Mills Jr., A.P., Yurke, B., Platzman, P.M.: Article for analog vector algebra computation. In: Kari, L., Rubin, H., Wood, D.H. (eds.) Proceedings 4th DIMACS Workshop on DNA Based Computers, University of Pennysylvania, Philadelphia, pp. 175–180 (1998)Google Scholar
- 32.Mir, K.U.: A Restricted Genetic Alphabet for DNA Computing. In: Proceedings of the Second Annual Meeting on DNA Based Computers, Princeton University (1996); Landwaber, L., Baum, E. (eds.): DNA based computer II. DIMACS series in Discrete Math. and Theoretical Comp. Sci, vol. 44 (1999)Google Scholar
- 33.Nevill-Manning, C.G., Witten, I.H.: Protein is Incompressible. In: IEEE Data Compression Conference, pp. 257–266. IEEE Computer Society TCC, Los Alamitos (1999)Google Scholar
- 34.Orlian, M., Guarnieri, F., Bancroft, C.: Parallel Primer Extension Horizontal Chain Reactions as a Paradigm of Parallel DNA-Based Computation. In: Rubin, H., Wood, D. (eds.) DNA based computer III. DIMACS series in Discrete Math. and Theoretical Comp. Sci, vol. 48, pp. 142–158 (1999)Google Scholar
- 35.Pease, A.C., Solas, D., Sullivan, E.J., Cronin, M.T., Holmes, C.P., Fodor, S.P.: Light-generated oligonucleotide arrays for rapid DNA sequence analysis. Proc. Natl Acad. Sci. USA 91, 5022–5026 (1994)CrossRefGoogle Scholar
- 36.Reif, J.H.: Local Parallel Biomolecular Computing. In: Rubin, H., Wood, D. (eds.) DNA based computer III. DIMACS series in Discrete Math. and Theoretical Comp. Sci, vol. 48, pp. 243–264 (1999)Google Scholar
- 37.Reif, J.H.: Paradigms for Biomolecular Computation. In: Calude, C.S., Casti, J., Dinneen, M.J. (eds.) Unconventional Models of Computation. Springer, Heidelberg (1998)Google Scholar
- 38.Reif, J.H.: Parallel Molecular Computation: Models and Simulations. Algorithmica, Special Issue on Computational Biology (1998)Google Scholar
- 39.Roberts, S.S.: Turbocharged PCR. Jour. of N.I.H. Research 6, 46–82 (1994)Google Scholar
- 40.Rose, J.A., Deaton, R., Garzon, M., Murphy, R.C., Franceschetti, D.R., Stevens Jr., S.E.: The effect of uniform melting temperatures on the efficiency of DNA computing. In: Rubin, H., Wood, D. (eds.) DNA based computer III. DIMACS series in Discrete Math. and Theoretical Comp. Sci., vol. 48, pp. 35–42 (1999)Google Scholar
- 41.Roweis, S., Winfree, E., Burgoyne, R., Chelyapov, N.V., Goodman, M.F., Rothemund, P.W.K., Adleman, L.M.: A Sticker Based Architecture for DNA Computation. In: Landwaber, L., Baum, E. (eds.) DNA based computer II. DIMACS series in Discrete Math. and Theoretical Comp. Sci, vol. 44, pp. 1–29 (1999)Google Scholar
- 42.Schneier, B.: Applied Cryptography: Protocols, Algorithms, and Source Code in C. John Wiley & Sons, Inc., Chichester (1996)zbMATHGoogle Scholar
- 43.Storer, J.A.: Data Compression: Methods and Theory. Computer Science Press, Rockville (1988)Google Scholar
- 44.Suyama, A.: DNA chips - Integrated Chemical Circuits for DNA Diagnosis and DNA computers (1998)Google Scholar
- 45.Taylor, C.T., Risca, V., Bancroft, C.: Hiding messages in DNA microdots. Nature 399, 533–534 (1999)CrossRefGoogle Scholar
- 46.Winfree, E.: On the Computational Power of DNA Annealing and Ligation. In: Baum, E.B., Lipton, R.J. (eds.) DNA Based Computers. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, pp. 187–198. American Mathematical Society, Providence (1995)Google Scholar
- 47.Winfree, E.: Complexity of Restricted and Unrestricted Models of Molecular Computation. In: Baum, E.B., Lipton, R.J. (eds.) DNA Based Computers. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, vol. 27, pp. 187–198. American Mathematical Society, Providence (1995)Google Scholar
- 48.Winfree, E.: Simulations of Computing by Self-Assembly. In: Proceedings of the Fourth DIMACS Meeting on DNA Based Computing, pp. 213–242 (1998)Google Scholar
- 49.Winfree, E., Liu, F., Wenzler, L.A., Seeman, N.C.: Design and Self-Assembly of Two Dimensional DNA Crystals. Nature 394, 539–544 (1998)CrossRefGoogle Scholar
- 50.Winfree, E., Yang, X., Seeman, N.C.: Universal Computation via Self-assembly of DNA: Some Theory and Experiments. In: Landwaber, L., Baum, E. (eds.) DNA based computer II. DIMACS series in Discrete Math. and Theoretical Comp. Sci, vol. 44, pp. 191–214 (1999)Google Scholar
- 51.Ziv, J., Lempel, A.: A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory IT-23, 337–343 (1977)Google Scholar