Skip to main content
SpringerLink
Log in

Seeing through Mist Given a Small Fraction of an RSA Private Key

  • Conference paper
  • First Online:
Topics in Cryptology — CT-RSA 2003 (CT-RSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2612))

Included in the following conference series:

Abstract

In smartcard encryption and signature applications, randomised algorithms are used to increase tamper resistance against attacks based on side channel leakage. Mist is one of these. As is the case with the classical m-ary and slidingwin dows exponentiation algorithms, the most significant half of the public modulus yields information which can be used to halve the number of key digits which need to be guessed to recover the secret key from a Mist side channel trace. Lattice based methods are used to reduce this to just one quarter of the least significant digits. This enables the strength of the Mist exponentiation algorithm to be guaged more accurately under several threat models.

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. D. Agrawal, B. Archambeault, J.R. Rao & P. Rohatgi, The EM Side-Channels, Cryptographic Hardware and Embedded Systems-CHES 2002, B. Kaliski, /cC. Koç & C. Paar (editors), LNCS 2523, Springer-Verlag, 2002, to appear. 391

    Google Scholar 

  2. D. Boneh, G. Durfee & Y. Frankel, Exposing an RSA Private Key Given a Small Fraction of its Bits, Advances in Cryptology-AsiaCrypt’ 98, K. Ohta & D. Pei (editors), LNCS 1514, Springer-Verlag, 1998, 25–34. 392, 398, 399, 400

    Chapter  Google Scholar 

  3. D. Coppersmith, Small Solutions to Polynomial equations and low exponent RSA vulnerabilities, Journal of Cryptology 10 (1997), 233–260. 398

    Article  MATH  MathSciNet  Google Scholar 

  4. K. Gandolfi, C. Mourtel & F. Olivier, Electromagnetic Analysis: Concrete Results, Cryptographic Hardware and Embedded Systems-CHES 2001, Ç. Koç, D. Naccache & C. Paar (editors), LNCS 2162, Springer-Verlag, 2001, 251–261. 391

    Chapter  Google Scholar 

  5. J.C. Ha & S. J. Moon, Randomized signed-scalar multiplication of ECC to resist power attacks, Cryptographic Hardware and Embedded Systems-CHES 2002, B. Kaliski, Ç. Koç & C. Paar (editors), LNCS 2523, Springer-Verlag, 2002, to appear. 392

    Google Scholar 

  6. K. Itoh, J. Yajima, M. Takenaka, & N. Torii, DPA Countermeasures by improving the window method, Cryptographic Hardware and Embedded Systems-CHES 2002, B. Kaliski, Ç. Koç & C. Paar (editors), LNCS 2523, Springer-Verlag, 2002, to appear. 392

    Google Scholar 

  7. D.E. Knuth, The Art of Computer Programming, vol. 2, “Seminumerical Algorithms”, 2nd Edition, Addison-Wesley, 1981, 441–466. 392

    Google Scholar 

  8. P. Kocher, Timing Attack on Implementations of Diffie-Hellman, RSA, DSS, and other systems, Advances in Cryptology-Crypto’ 96, N. Koblitz (editor), LNCS 1109, Springer-Verlag, 1996, 104–113. 391, 395

    Chapter  Google Scholar 

  9. P. Kocher, J. Jaffe & B. Jun, Differential Power Analysis, Advances in Cryptology-Crypto’ 99, M. Wiener (editor), LNCS 1666, Springer-Verlag, 1999, 388–397. 391, 393

    Google Scholar 

  10. R. Kumanduri & C. Romero, Number Theory with Computer Applications, Prentice Hall, 1998, ISBN 0-13-801812-X. 399

    Google Scholar 

  11. P.-Y. Liardet & N.P. Smart, Preventing SPA/DPA in ECC Systems using the Jacobi Form, Cryptographic Hardware and Embedded Systems-CHES 2001, Ç. Koç, D. Naccache & C. Paar (editors), LNCS 2162, Springer-Verlag, 2001, 391–401. 392

    Chapter  Google Scholar 

  12. T. S. Messerges, E.A. Dabbish & R.H. Sloan, Power Analysis Attacks of Modular Exponentiation in Smartcards, Cryptographic Hardware and Embedded Systems (Proc. CHES 99), C. Paar & Ç. Koç (editors), LNCS 1717, Springer-Verlag, 1999, 144–157. 391

    Chapter  Google Scholar 

  13. K. Okeya & K. Sakurai, On Insecurity of the Side Channel Attack Countermeasure using Addition-Subtraction Chains under Distinguishability between Addition and Doubling, Information Security and Privacy, L. Batten & J. Seberry (editors), LNCS 2384, Springer-Verlag, 2002, 420–435. 392

    Chapter  Google Scholar 

  14. E. Oswald & M. Aigner, Randomized Addition-Subtraction Chains as a Countermeasure against Power Attacks, Cryptographic Hardware and Embedded Systems-CHES 2001, Ç. Koç, D. Naccache & C. Paar (editors), LNCS 2162, Springer-Verlag, 2001, 39–50. 392

    Chapter  Google Scholar 

  15. J.-J. Quisquater & D. Samyde, ElectroMagnetic Analysis (EMA): Measures and Counter-Measures for Smart Cards, Smart Card Programming and Security (e-Smart 2001), LNCS 2140, Springer-Verlag, 2001, 200–210. 391, 393

    Chapter  Google Scholar 

  16. J.-J. Quisquater & D. Samyde, Eddy current for Magnetic Analysis with Active Sensor, Proc. e-Smart 2002, Nice, September 2002, 183–194. 391

    Google Scholar 

  17. C. D. Walter & S. Thompson, Distinguishing Exponent Digits by Observing Modular Subtractions, Topics in Cryptology-CT-RSA 2001, D. Naccache (editor), LNCS 2020, Springer-Verlag, 2001, 192–207. 391

    Chapter  Google Scholar 

  18. C.D. Walter, Sliding Windows succumbs to Big Mac Attack, Cryptographic Hardware and Embedded Systems-CHES 2001, Ç. Koç, D. Naccache & C. Paar (editors), LNCS 2162, Springer-Verlag, 2001, 286–299. 391

    Chapter  Google Scholar 

  19. C.D. Walter, Precise Bounds for Montgomery Modular Multiplication and Some Potentially Insecure RSA Moduli, Topics in Cryptology-CT-RSA 2002, B. Preneel (editor), LNCS 2271, Springer-Verlag, 2001, 30–39. 391

    Chapter  Google Scholar 

  20. C.D. Walter, Improvements in, and relating to, Cryptographic Methods and Apparatus, UK Patent Application 0126317.7, Comodo Research Laboratory, 2001. 392

    Google Scholar 

  21. C.D. Walter, MIST: An Efficient, Randomized Exponentiation Algorithm for Resisting Power Analysis, Topics in Cryptology-CT-RSA 2002, B. Preneel (editor), LNCS 2271, Springer-Verlag, 2002, 53–66. 392, 393

    Chapter  Google Scholar 

  22. C.D. Walter, Some Security Aspects of the MIST Randomized Exponentiation Algorithm, Cryptographic Hardware and Embedded Systems-CHES 2002, B. Kaliski, Ç. Koç & C. Paar (editors), LNCS 2523, Springer-Verlag, 2002, to appear. 392, 393, 396, 400

    Google Scholar 

  23. C.D. Walter, Breaking the Liardet-Smart Randomized Exponentiation Algorithm, Proc. Cardis’ 02, USENIX, to appear. 392

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Comodo Research Lab, 10 Hey Street, BD7 1DQ, Bradford, UK

    Colin D. Walter

Authors
  1. Colin D. Walter
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Gemplus, Card Security Group, La Vigie, Avenue du Jujubier, ZI Athélia IV, 13705, La Ciotat Cedex, France

    Marc Joye

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Walter, C.D. (2003). Seeing through Mist Given a Small Fraction of an RSA Private Key. In: Joye, M. (eds) Topics in Cryptology — CT-RSA 2003. CT-RSA 2003. Lecture Notes in Computer Science, vol 2612. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36563-X_27

Download citation

  • DOI: https://doi.org/10.1007/3-540-36563-X_27

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00847-7

  • Online ISBN: 978-3-540-36563-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation