Skip to main content
Top

2015 | OriginalPaper | Chapter

Toward Secure Implementation of McEliece Decryption

Authors : Mariya Georgieva, Frédéric de Portzamparc

Published in: Constructive Side-Channel Analysis and Secure Design

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We analyse the security regarding timing attacks of implementations of the decryption in McEliece PKC with binary Goppa codes. First, we review and extend the existing attacks, both on the messages and on the keys. We show that, until now, no satisfactory countermeasure could erase all the timing leakages in the Extended Euclidean Algorithm (EEA) step. Then, we describe a version of the EEA never used for McEliece so far. It uses a constant number of operations for given public parameters. In particular, the operation flow does not depend on the input of the decryption, and thus closes all previous timing attacks. We end up with what should become a central tool toward a secure implementation of McEliece decryption.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Avanzi, R., Hoerder, S., Page, D., Tunstall, M.: Side-channel attacks on the McEliece and Niederreiter public-key cryptosystems. J. Cryptographic Eng. 1(4), 271–281 (2011)CrossRef Avanzi, R., Hoerder, S., Page, D., Tunstall, M.: Side-channel attacks on the McEliece and Niederreiter public-key cryptosystems. J. Cryptographic Eng. 1(4), 271–281 (2011)CrossRef
2.
go back to reference Berlekamp, E., McEliece, R., van Tilborg, H.: On the inherent intractability of certain coding problems. IEEE Trans. Inf. Theory 24(3), 384–386 (1978)CrossRefMATH Berlekamp, E., McEliece, R., van Tilborg, H.: On the inherent intractability of certain coding problems. IEEE Trans. Inf. Theory 24(3), 384–386 (1978)CrossRefMATH
3.
go back to reference Berlekamp, E., Seroussi, G., Po, T.: A hypersystolic reed–solomon decoder. In: Bhargava, V.K., Wicker, S.B., IEEE Communications Society, IEEE Information Theory Society (eds.) Reed-Solomon Codes and Their Applications, pp. 205–241. IEEE Press, Piscataway (1994) Berlekamp, E., Seroussi, G., Po, T.: A hypersystolic reed–solomon decoder. In: Bhargava, V.K., Wicker, S.B., IEEE Communications Society, IEEE Information Theory Society (eds.) Reed-Solomon Codes and Their Applications, pp. 205–241. IEEE Press, Piscataway (1994)
4.
go back to reference Bernstein, D.J., Chou, T., Schwabe, P.: McBits: fast constant-time code-based cryptography. In: Bertoni, G., Coron, J.-S. (eds.) CHES 2013. LNCS, vol. 8086, pp. 250–272. Springer, Heidelberg (2013) CrossRef Bernstein, D.J., Chou, T., Schwabe, P.: McBits: fast constant-time code-based cryptography. In: Bertoni, G., Coron, J.-S. (eds.) CHES 2013. LNCS, vol. 8086, pp. 250–272. Springer, Heidelberg (2013) CrossRef
5.
go back to reference Biswas, B.: Aspects de mise en oeuvre de la cryptographie basée sur les codes. These, Ecole Polytechnique X, October 2010 Biswas, B.: Aspects de mise en oeuvre de la cryptographie basée sur les codes. These, Ecole Polytechnique X, October 2010
6.
go back to reference Heyse, S.: Implementation of McEliece based on quasi-dyadic goppa codes for embedded devices. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 143–162. Springer, Heidelberg (2011) CrossRef Heyse, S.: Implementation of McEliece based on quasi-dyadic goppa codes for embedded devices. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 143–162. Springer, Heidelberg (2011) CrossRef
7.
go back to reference MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes, 5th edn. North-Holland, Amsterdam (1986) MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes, 5th edn. North-Holland, Amsterdam (1986)
8.
go back to reference Overbeck, R., Sendrier, N.: Code-based cryptography. In: Bernstein, D., Buchmann, J., Dahmen, E. (eds.) Post-Quantum Cryptography, pp. 95–145. Springer, Heidelberg (2009)CrossRef Overbeck, R., Sendrier, N.: Code-based cryptography. In: Bernstein, D., Buchmann, J., Dahmen, E. (eds.) Post-Quantum Cryptography, pp. 95–145. Springer, Heidelberg (2009)CrossRef
9.
go back to reference Patterson, N.: The algebraic decoding of Goppa codes. IEEE Trans. Inf. Theory 21(2), 203–207 (1975)CrossRef Patterson, N.: The algebraic decoding of Goppa codes. IEEE Trans. Inf. Theory 21(2), 203–207 (1975)CrossRef
10.
go back to reference Sarwate, D., Shanbhag, N.: High-speed architectures for Reed-Solomon decoders. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 9(5), 641–655 (2001)CrossRef Sarwate, D., Shanbhag, N.: High-speed architectures for Reed-Solomon decoders. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 9(5), 641–655 (2001)CrossRef
11.
go back to reference Sarwate, D., Yan, Z.: Modified Euclidean algorithms for decoding Reed-Solomon codes. In: IEEE International Symposium on Information Theory, ISIT 2009, pp. 1398–1402, June 2009 Sarwate, D., Yan, Z.: Modified Euclidean algorithms for decoding Reed-Solomon codes. In: IEEE International Symposium on Information Theory, ISIT 2009, pp. 1398–1402, June 2009
12.
go back to reference Shoufan, A., Strenzke, F., Molter, H.G., Stöttinger, M.: A timing attack against patterson algorithm in the McEliece PKC. In: Lee, D., Hong, S. (eds.) ICISC 2009. LNCS, vol. 5984, pp. 161–175. Springer, Heidelberg (2010) CrossRef Shoufan, A., Strenzke, F., Molter, H.G., Stöttinger, M.: A timing attack against patterson algorithm in the McEliece PKC. In: Lee, D., Hong, S. (eds.) ICISC 2009. LNCS, vol. 5984, pp. 161–175. Springer, Heidelberg (2010) CrossRef
13.
go back to reference Shoufan, A., Wink, T., Molter, H., Huss, S., Kohnert, E.: A Novel cryptoprocessor architecture for the McEliece public-key cryptosystem. IEEE Trans. Comput. 59(11), 1533–1546 (2010)MathSciNetCrossRef Shoufan, A., Wink, T., Molter, H., Huss, S., Kohnert, E.: A Novel cryptoprocessor architecture for the McEliece public-key cryptosystem. IEEE Trans. Comput. 59(11), 1533–1546 (2010)MathSciNetCrossRef
14.
go back to reference Strenzke, F.: A smart card implementation of the McEliece PKC. In: Samarati, P., Tunstall, M., Posegga, J., Markantonakis, K., Sauveron, D. (eds.) WISTP 2010. LNCS, vol. 6033, pp. 47–59. Springer, Heidelberg (2010) Strenzke, F.: A smart card implementation of the McEliece PKC. In: Samarati, P., Tunstall, M., Posegga, J., Markantonakis, K., Sauveron, D. (eds.) WISTP 2010. LNCS, vol. 6033, pp. 47–59. Springer, Heidelberg (2010)
15.
go back to reference Strenzke, F.: A timing attack against the secret permutation in the McEliece PKC. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 95–107. Springer, Heidelberg (2010) CrossRef Strenzke, F.: A timing attack against the secret permutation in the McEliece PKC. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 95–107. Springer, Heidelberg (2010) CrossRef
16.
go back to reference Strenzke, F.: Timing attacks against the syndrome inversion in Code-Based cryptosystems. In: Gaborit, P. (ed.) PQCrypto 2013. LNCS, vol. 7932, pp. 217–230. Springer, Heidelberg (2013) CrossRef Strenzke, F.: Timing attacks against the syndrome inversion in Code-Based cryptosystems. In: Gaborit, P. (ed.) PQCrypto 2013. LNCS, vol. 7932, pp. 217–230. Springer, Heidelberg (2013) CrossRef
17.
go back to reference Strenzke, F., Tews, E., Molter, H.G., Overbeck, R., Shoufan, A.: Side channels in the McEliece PKC. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 216–229. Springer, Heidelberg (2008) CrossRef Strenzke, F., Tews, E., Molter, H.G., Overbeck, R., Shoufan, A.: Side channels in the McEliece PKC. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 216–229. Springer, Heidelberg (2008) CrossRef
18.
go back to reference Sugiyama, Y., Kasahara, M., Hirasawa, S., Namekawa, T.: A method for solving key equation for decoding goppa codes. Inf. Control 27(1), 87–99 (1975)MathSciNetCrossRefMATH Sugiyama, Y., Kasahara, M., Hirasawa, S., Namekawa, T.: A method for solving key equation for decoding goppa codes. Inf. Control 27(1), 87–99 (1975)MathSciNetCrossRefMATH
19.
go back to reference Thull, K., Yap, C.: A Unified Approach to HGCD Algorithms for polynomials and integers (1990) Thull, K., Yap, C.: A Unified Approach to HGCD Algorithms for polynomials and integers (1990)
Metadata
Title
Toward Secure Implementation of McEliece Decryption
Authors
Mariya Georgieva
Frédéric de Portzamparc
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-21476-4_10

Premium Partner