Skip to main content
SpringerLink
Log in

The Modular Inversion in GF(p) by Self-assembling and Its Application to Elliptic Curve Diffie-Hellman Key Exchange

  • Conference paper
Bio-Inspired Computing - Theories and Applications

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 472))

  • 1359 Accesses

Abstract

The study of tile self-assembly model shows the development of self-assembling systems for solving complex computational problems. In this paper, we show the method of performing modular inversion in GF(p) by self-assembling with Θ(p) computational tile types in Θ(p) steps. Then, we discuss how the self-assembling systems for computing modular inversion in GF(p) apply to elliptic curve Diffie-Hellman key exchange algorithm. The self-assembled architectures provide the feasibility of cryptanalysis for this algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adleman, L.M.: Molecular Computation of Solutions to Combinatorial Problems. Science 266, 1021–1024 (1994)

    Article  Google Scholar 

  2. Pan, L., Wang, J., Hoogeboom, H.J.: Spiking Neural P Systems with Astrocytes. Neural Computation 24, 805–825 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Pan, L., Zeng, X.: Small Universal Spiking Neural P Systems Working in Exhaustive Mode. IEEE Transactions on Nanobioscience 10, 99–105 (2011)

    Article  Google Scholar 

  4. Pan, L., Pérez-Jiménez, M.J.: Computational Complexity of Tissue-like P Systems. J. Complexity 26, 296–315 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Seeman, N.C.: DNA Nanotechnology: Novel DNA Constructions. Annu. Rev. Biophy. Biomol. Struct. 27, 225–248 (1998)

    Article  Google Scholar 

  6. Barish, R., Rothemund, P.W., Winfree, E.: Two Computational Primitives for Algorithmic Self-assembly: Copying and Counting. Nano Lett. 12, 2586–2592 (2005)

    Article  Google Scholar 

  7. Rothemund, P.W.: Folding DNA to Create Nanoscale Shapes and Patterns. Nature 440, 297–302 (2006)

    Article  Google Scholar 

  8. Lathrop, J.I., Lutz, J.H., Summers, S.M.: Strict Self-assembly of Discrete Sierpinski Triangles. Theor. Comput. Sci. 410, 384–405 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ke, Y., Ong, L.L., Shih, W.M., et al.: Three-dimensional Structures Self-assembled from DNA Bricks. Science 6111, 1177–1183 (2012)

    Article  Google Scholar 

  10. Mao, C., LaBean, T.H., Reif, J.H.: Logical Computation using Algorithmic Self-assembly of DNA Triple-crossover Molecules. Nature 407, 493–496 (2000)

    Article  Google Scholar 

  11. Brun, Y.: Arithmetic Computation in the Tile Assembly Model: Addition and Multiplication. Theor. Comput. Sci. 378, 17–31 (2006)

    Article  MathSciNet  Google Scholar 

  12. Brun, Y.: Nondeterministic Polynomial Time Factoring in the Tile Assembly Model. Theor. Comput. Sci. 395, 3–23 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cheng, Z.: Nondeterministic Algorithm for Breaking Diffie-Hellman Key Exchange using Self-assembly of DNA Tiles. Int. J. Comput. Commun. 7, 616–630 (2012)

    Google Scholar 

  14. Marcelo, E.K., Takagi, N.: A Hardware Algorithm for Modular Multiplication/division. IEEE Transactions on Computers 54, 12–21 (2005)

    Article  Google Scholar 

  15. Koblitz, N.: Elliptic Curve Cryptosystem. Math. Comp. 48, 203–209 (1987)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Zhejiang University of Technology, Hangzhou, 310023, China

    Zhen Cheng & Yufang Huang

  2. College of Maths, Southwest Jiaotong University, Chengdu, 610031, China

    Zhen Cheng & Yufang Huang

Authors
  1. Zhen Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yufang Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Huazhong University of Science and Technology, 430074, Wuhan, China

    Linqiang Pan

  2. Institute of Mathematics of the Romanian Academy, 014700, Bucuresti, Romania

    Gheorghe Păun

  3. Department of Computer Science and Artificial Intelligence, University of Sevilla, Avda. Reina Mercedes s/n., 41012, Sevilla, Spain

    Mario J. Pérez-Jiménez

  4. School of Automation, Huazhong University of Science and Technology, 430074, Wuhan, China

    Tao Song

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cheng, Z., Huang, Y. (2014). The Modular Inversion in GF(p) by Self-assembling and Its Application to Elliptic Curve Diffie-Hellman Key Exchange. In: Pan, L., Păun, G., Pérez-Jiménez, M.J., Song, T. (eds) Bio-Inspired Computing - Theories and Applications. Communications in Computer and Information Science, vol 472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45049-9_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-45049-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-45048-2

  • Online ISBN: 978-3-662-45049-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation