Skip to main content
SpringerLink
Log in

On the Use of Shamir’s Secret Sharing against Side-Channel Analysis

  • Conference paper
Smart Card Research and Advanced Applications (CARDIS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7771))

Abstract

At CHES 2011 Goubin and Martinelli described a new countermeasure against side-channel analysis for AES based on Shamir’s secret-sharing scheme. In the present paper, we exhibit a flaw in this scheme and we show that it is always theoretically broken by a first-order side-channel analysis. As a consequence of this attack, only a slight adaptation of the scheme proposed by Ben-Or et al.at STOC in 1988 can securely process multiplications on data shared with Shamir’s technique. In the second part of this paper, we propose an improvement of this scheme that leads to a complexity \({\cal \tilde O}(d^2)\) instead of \({\cal O}(d^3)\), where d is the number of shares per data.

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. Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: Simon, J. (ed.) STOC, pp. 1–10. ACM (1988)

    Google Scholar 

  2. Blömer, J., Guajardo, J., Krummel, V.: Provably Secure Masking of AES. In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 69–83. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  3. Carlet, C., Goubin, L., Prouff, E., Quisquater, M., Rivain, M.: Higher-order masking schemes for S-boxes. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 366–384. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  4. Chari, S., Jutla, C., Rao, J., Rohatgi, P.: A Cautionary Note Regarding Evaluation of AES Candidates on Smart-Cards. In: Second AES Candidate Conference – AES 2 (March 1999)

    Google Scholar 

  5. Coron, J.-S., Prouff, E., Rivain, M.: Side Channel Cryptanalysis of a Higher Order Masking Scheme. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 28–44. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Courtois, N., Goubin, L.: An Algebraic Masking Method to Protect AES against Power Attacks. In: Won, D., Kim, S. (eds.) ICISC 2005. LNCS, vol. 3935, pp. 199–209. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Damgård, I., Ishai, Y., Krøigaard, M., Nielsen, J.B., Smith, A.: Scalable multiparty computation with nearly optimal work and resilience. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 241–261. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Fumaroli, G., Martinelli, A., Prouff, E., Rivain, M.: Affine masking against higher-order side channel analysis. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 262–280. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  9. Genelle, L., Prouff, E., Quisquater, M.: Thwarting Higher-Order Side Channel Analysis with Additive and Multiplicative Maskings. In: Preneel, Takagi (eds.) [19], pp. 240–255

    Google Scholar 

  10. Gennaro, R., Rabin, M.O., Rabin, T.: Simplified vss and fact-track multiparty computations with applications to threshold cryptography. In: PODC, pp. 101–111 (1998)

    Google Scholar 

  11. Goubin, L., Martinelli, A.: Protecting aes with shamir’s secret sharing scheme. In: Preneel, Takagi (eds.) [19], pp. 79–94

    Google Scholar 

  12. Ishai, Y., Sahai, A., Wagner, D.: Private Circuits: Securing Hardware against Probing Attacks. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 463–481. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Kim, H., Hong, S., Lim, J.: A Fast and Provably Secure Higher-Order Masking of AES S-Box. In: Preneel, Takagi (eds.) [19], pp. 95–107

    Google Scholar 

  14. Kocher, P., Jaffe, J., Jun, B.: Introduction to Differential Power Analysis and Related Attacks. Technical report, Cryptography Research Inc. (1998)

    Google Scholar 

  15. Oswald, E., Mangard, S., Herbst, C., Tillich, S.: Practical Second-order DPA Attacks for Masked Smart Card Implementations of Block Ciphers. In: Pointcheval (ed.) [18], pp. 192–207

    Google Scholar 

  16. Oswald, E., Mangard, S., Pramstaller, N., Rijmen, V.: A Side-Channel Analysis Resistant Description of the AES S-box. In: Gilbert, H., Handschuh, H. (eds.) FSE 2005. LNCS, vol. 3557, pp. 413–423. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  17. Peeters, E., Standaert, F.-X., Donckers, N., Quisquater, J.-J.: Improved Higher-order Side-Channel Attacks with FPGA Experiments. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 309–323. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. Pointcheval, D. (ed.): CT-RSA 2006. LNCS, vol. 3860. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  19. Preneel, B., Takagi, T. (eds.): CHES 2011. LNCS, vol. 6917. Springer, Heidelberg (2011)

    MATH  Google Scholar 

  20. Prouff, E., Roche, T.: Higher-order glitches free implementation of the aes using secure multi-party computation protocols. In: Preneel, Takagi (eds.) [19], pp. 63–78

    Google Scholar 

  21. Rivain, M., Prouff, E.: Provably Secure Higher-Order Masking of AES. In: Mangard, S., Standaert, F.-X. (eds.) CHES 2010. LNCS, vol. 6225, pp. 413–427. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  22. Roche, T., Prouff, E.: Higher-order glitch free implementation of the aes using secure multi-party computation protocols. Journal of Cryptographic Engineering, 1–17 (2012)

    Google Scholar 

  23. Satoh, A., Morioka, S., Takano, K., Munetoh, S.: A Compact Rijndael Hardware Architecture with S-Box Optimization. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 239–254. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  24. Schramm, K., Paar, C.: Higher Order Masking of the AES. In: Pointcheval (ed.) [18], pp. 208–225

    Google Scholar 

  25. Shamir, A.: How to Share a Secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  26. Standaert, F.-X., Veyrat-Charvillon, N., Oswald, E., Gierlichs, B., Medwed, M., Kasper, M., Mangard, S.: The World Is Not Enough: Another Look on Second-Order DPA. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 112–129. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  27. Waddle, J., Wagner, D.: Towards Efficient Second-Order Power Analysis. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 1–15. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  28. Wang, Y., Zhu, X.: A fast algorithm for the fourier transform over finite fields and its vlsi implementation. IEEE Journal on Selected Areas in Communications 6(3), 572–577 (1988)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tranef, France

    Jean-Sébastien Coron

  2. ANSSI, 51, Bd de la Tour-Maubourg, 75700, Paris 07 SP, France

    Emmanuel Prouff & Thomas Roche

Authors
  1. Jean-Sébastien Coron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Emmanuel Prouff
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas Roche
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Infineon Technologies AG, Am Campeon 1-12, 85579, Neubiberg, Germany

    Stefan Mangard

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Coron, JS., Prouff, E., Roche, T. (2013). On the Use of Shamir’s Secret Sharing against Side-Channel Analysis. In: Mangard, S. (eds) Smart Card Research and Advanced Applications. CARDIS 2012. Lecture Notes in Computer Science, vol 7771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37288-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-37288-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37287-2

  • Online ISBN: 978-3-642-37288-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation