Skip to main content
SpringerLink
Log in

On the Multiple Fault Attacks on RSA Signatures with LSBs of Messages Unknown

  • Conference paper
Information Security and Cryptology (Inscrypt 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7763))

Included in the following conference series:

  • 1102 Accesses

Abstract

In CHES 2009, Coron, Joux, Kizhvatov, Naccache and Paillier (CJKNP) introduced the multiple fault attack on RSA signatures with partially unknown messages. However, the complexity of their attack is exponential in the number of faulty signatures. At RSA 2010, this fault attack was improved, which runs in polynomial time in the number of faults. Both of the previous fault attacks deal with the general case. This paper considers the special situation that some least significant bits (LSBs) of messages are unknown. Because of this special case, our new multiple fault attack can handle a larger size of the unknown part of message. We provide two kinds of techniques to factor the RSA modulus N using the multiple faulty signatures. Comparisons between the previous attacks and the new attacks with a number of LSBs of the message unknown are given on the basis of the simulations.

Supported by the National Natural Science Foundation of China (Grant No.61133013) and the National Basic Research Program of China (Grant No. 2013CB834205).

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. Boneh, D., DeMillo, R.A., Lipton, R.J.: On the Importance of Checking Cryptographic Protocols for Faults. Journal of Cryptology 14(2), 101–119 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cohn, H., Heninger, N.: Approximate Common Divisiors Via Lattices. Cryptology ePrint Archive, Report 2011/437, http://eprint.iacr.org/2011/437

  3. Coppersmith, D.: Small Solutions to Polynomial Equations, and Low Exponent Vulnerabilities. Journal of Cryptology 10(4), 233–260 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Coron, J.-S., Joux, A., Kizhvatov, I., Naccache, D., Paillier, P.: Fault Attacks on RSA Signatures with Partially Unknown Messages. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 444–456. Springer, Heidelberg (2009), Full version: eprint.iacr.org/2009/309

    Chapter  Google Scholar 

  5. Coron, J.-S., Naccache, D., Tibouchi, M.: Fault Attacks Against emv Signatures. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 208–220. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  6. Coron, J.-S., Naccache, D., Tibouchi, M., Weinmann, R.-P.: Practical Cryptanalysis of iso/iec 9796-2 and emv Signatures. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 428–444. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Jochemsz, E., May, A.: A Strategy for Finding Roots of Multivariate Polynomials with New Applications in Attacking RSA Variants. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 267–282. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  8. Howgrave-Graham, N.: Approximate integer common divisors. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 51–66. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. ISO/IEC 9796-2, Information Technology-Security Techniques-Digital Signature Schemes Giving Message Recovery-Part 2: Mechanisms Using a Hash-Funcion (1997)

    Google Scholar 

  10. ISO/IEC 9796-2: 2002 Information Technology-Security Techniques-Digital Signature Schemes Giving Message Recovery-Part 2: Integer Factorization Based Mechanisms (2002)

    Google Scholar 

  11. Lenstra, A., Lenstra Jr., H., Lovász, L.: Factoring Polynomials with Rational Coefficients. Mathematische Annalen 261, 513–534 (1982)

    Article  Google Scholar 

  12. Nguyen, P., Stern, J.: Cryptanalysis of a fast public key cryptosystem presented at SAC ’97. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 213–218. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  13. Rivest, R., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public Key Cryptosystems. Communications of the ACM, 120–126 (1978)

    Google Scholar 

  14. Shoup, V.: Number Theory C++ Library (NTL) version version 5.5.2, http://www.shoup.net/ntl/

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Hangzhou Normal University, Hangzhou, 310036, China

    Lidong Han

  2. Institute for Advanced Study, Tsinghua University, Beijing, 100084, China

    Lidong Han, Wei Wei & Mingjie Liu

  3. Beijing International Center for Mathematical Research, Peking University, Beijing, 100084, China

    Mingjie Liu

Authors
  1. Lidong Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mingjie Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Fundamental Problems of Technology, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Mirosław Kutyłowski

  2. Computer Science Department, Columbia University and Google Inc., Amsterdam Avenue 1214, 10027, New York, NY, USA

    Moti Yung

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Han, L., Wei, W., Liu, M. (2013). On the Multiple Fault Attacks on RSA Signatures with LSBs of Messages Unknown. In: Kutyłowski, M., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2012. Lecture Notes in Computer Science, vol 7763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38519-3_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38519-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38518-6

  • Online ISBN: 978-3-642-38519-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation