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International Conference on Information Security

ISC 2012: Information Security pp 120–135Cite as

Solutions for the Storage Problem of McEliece Public and Private Keys on Memory-Constrained Platforms

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7483))

Abstract

While it is generally believed that due to their large public and private key sizes code based public key schemes like the McEliece PKC cannot be conveniently implemented on memory-constrained devices, we demonstrate otherwise. We show that for the public key we face rather a transmission problem than a storage problem: we propose an approach for Public Key Infrastructure (PKI) scenarios which totally eliminates the need to store public keys of communication partners. Instead, all the necessary computation steps are performed during the transmission of the key. We show the feasibility of the approach through an example implementation and give arguments that it will be possible for a smart card controller to carry out the associated computations fast enough to sustain the transmission rates of possible future high speed contactless interfaces. Concerning the McEliece private key, we demonstrate, contrasting to previously published implementations, that the parity check matrix, which is by far the largest part of this key, is not necessary to achieve fast decryption on embedded systems.

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References

  1. McEliece, R.J.: A public key cryptosystem based on algebraic coding theory. DSN Progress Report 42-44, 114–116 (1978)

    Google Scholar 

  2. Niederreiter, H.: Knapsack-type cryptosystems and algebraic coding theory. Problems Control Inform. Theory 15(2), 159–166 (1986)

    MathSciNet  MATH  Google Scholar 

  3. Courtois, N.T., Finiasz, M., Sendrier, N.: How to Achieve a McEliece-Based Digital Signature Scheme. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 157–174. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  4. Kabatianskii, G., Krouk, E., Smeets, B.: A Digital Signature Scheme Based on Random Error-Correcting Codes. In: Darnell, M. (ed.) Cryptography and Coding 1997. LNCS, vol. 1355, pp. 161–167. Springer, Heidelberg (1997)

    Google Scholar 

  5. Stern, J.: A New Identification Scheme Based on Syndrome Decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 13–21. Springer, Heidelberg (1994)

    Google Scholar 

  6. Bernstein, D.J., Buchmann, J., Dahmen, E.: Post Quantum Cryptography. Springer Publishing Company, Incorporated (2008)

    Google Scholar 

  7. Biswas, B., Sendrier, N.: McEliece Cryptosystem Implementation: Theory and Practice. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 47–62. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Berger, T.P., Cayrel, P.-L., Gaborit, P., Otmani, A.: Reducing Key Length of the McEliece Cryptosystem. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 77–97. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  9. Berger, T.P., Loidreau, P.: How to Mask the Structure of Codes for a Cryptographic Use. Designs, Codes and Cryptography 35, 63–79 (2005), doi:10.1007/s10623-003-6151-2

    Article  MathSciNet  MATH  Google Scholar 

  10. Misoczki, R., Barreto, P.S.L.M.: Compact McEliece Keys from Goppa Codes. In: Jacobson Jr., M.J., Rijmen, V., Safavi-Naini, R. (eds.) SAC 2009. LNCS, vol. 5867, pp. 376–392. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Otmani, A., Tillich, J.P., Dallot, L.: Cryptanalysis of Two McEliece Cryptosystems Based on Quasi-Cyclic Codes. Mathematics in Computer Science 3, 129–140 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Faugère, J.-C., Otmani, A., Perret, L., Tillich, J.-P.: Algebraic Cryptanalysis of McEliece Variants with Compact Keys. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 279–298. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  13. Umana, V.G., Leander, G.: Practical key recovery attacks on two McEliece variants. In: Cid, C., Faugere, J.-C. (eds.) SCC 2010, pp. 27–44 (2010)

    Google Scholar 

  14. Goppa, V.D.: A new class of linear correcting codes. Problems of Information Transmission 6, 207–212 (1970)

    MathSciNet  Google Scholar 

  15. Faugère, J.C., Otmani, A., Perret, L., Tillich, J.P.: A distinguisher for high rate McEliece cryptosystems. In: 2011 IEEE Information Theory Workshop (ITW), pp. 282–286. IEEE (2011)

    Google Scholar 

  16. Infineon Technologies AG: SLE76 Product Data Sheet, http://www.infineon.com/cms/de/product/channel.html?channel=db3a3043156fd57301161520ab8b1c4c

  17. Infineon Technologies AG: SLE 66CLX360PE(M) Family Data Sheet, http://www.infineon.com/dgdl/SPI_SLE66CLX360PE_1106.pdf?folderId=db3a304412b407950112b408e8c90004&fileId=db3a304412b407950112b4099d6c030a&location=Search.SPI_SLE66CLX360PE_1106.pdf

  18. Eisenbarth, T., Güneysu, T., Heyse, S., Paar, C.: MicroEliece: McEliece for Embedded Devices. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 49–64. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  19. 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)

    Chapter  Google Scholar 

  20. Heyse, S.: Low-Reiter: Niederreiter Encryption Scheme for Embedded Microcontrollers. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 165–181. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  21. Biswas, B., Sendrier, N.: HyMES - an open source implementation of the McEliece cryptosystem (2008), http://www-rocq.inria.fr/secret/CBCrypto/index.php?pg=hymes

  22. Shoufan, A., Wink, T., Molter, G., Huss, S., Strenzke, F.: A Novel Processor Architecture for McEliece Cryptosystem and FPGA Platforms. In: ASAP 2009, pp. 98–105. IEEE Computer Society, Washington, DC (2009)

    Google Scholar 

  23. German Federal Bureau of Information Security (BSI): Technical Guideline TR-03110: Advanced Security Mechanisms for Machine Readable Travel Documents, Version 2.02 (2009)

    Google Scholar 

  24. German Federal Bureau of Information Security (BSI): Technical Guideline TR-03111: Elliptic Curve Cryptography, Version 1.11 (2009)

    Google Scholar 

  25. MacWilliams, F.J., Sloane, N.J.A.: The theory of error correcting codes. North Holland (1997)

    Google Scholar 

  26. Kobara, K., Imai, H.: Semantically Secure McEliece Public-Key Cryptosystems - Conversions for McEliece PKC. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 19–35. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  27. Bernstein, D.J., Lange, T., Peters, C.: Attacking and Defending the McEliece Cryptosystem. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 31–46. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  28. Cooper, et al.: RFC 5280, http://tools.ietf.org/html/rfc5280

  29. Coronado, L.C., Buchmann, J., Carlos, L., Garcia, C., Dahmen, E., Klintsevich, E., Darmstadt, T.U.: CMSS – An Improved Merkle Signature Scheme Johannes Buchmann (2006), http://www.cdc.informatik.tu-darmstadt.de/~dahmen/papers/BCDDK06.pdf

  30. Witschnig, H., Patauner, C., Maier, A., Leitgeb, E., Rinner, D.: High speed RFID lab-scaled prototype at the frequency of 13.56 MHz. E & I Elektrotechnik und Informationstechnik 124, 376–383 (2007), doi:10.1007/s00502-007-0485-9

    Article  Google Scholar 

  31. Infineon Technologies AG: SLE78 Product Data Sheet, http://www.infineon.com/cms/en/product/channel.html?channel=db3a30431ce5fb52011d47b166342af0

  32. Gay, O., http://www.ouah.org/ogay/sha2/

  33. Kocher, P.C., Jaffe, J., Jun, B.: Differential Power Analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)

    Google Scholar 

  34. Overbeck, R., Sendrier, N.: Code-based cryptography. In: Bernstein, D., Buchmann, J., Dahmen, E. (eds.) Post-Quantum Cryptography, pp. 95–145. Springer (2009)

    Google Scholar 

  35. Finiasz, M.: Parallel-CFS: Strengthening the CFS McEliece-Based Signature Scheme. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 159–170. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  36. Otmani, A., Tillich, J.-P.: An Efficient Attack on All Concrete KKS Proposals. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 98–116. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  37. Bernstein, D.J.: List Decoding for Binary Goppa Codes. In: Chee, Y.M., Guo, Z., Ling, S., Shao, F., Tang, Y., Wang, H., Xing, C. (eds.) IWCC 2011. LNCS, vol. 6639, pp. 62–80. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. FlexSecure GmbH, Germany

    Falko Strenzke

Authors
  1. Falko Strenzke
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Editor information

Editors and Affiliations

  1. Institute of Security in Distributed Applications, University of Technology, Harburger Schlossstrasse 20, 21073, Hamburg, Germany

    Dieter Gollmann

  2. Department of Computer Science, University of Erlangen-Nürnberg, Am Wolfsmantel 46, 91058, Erlangen, Germany

    Felix C. Freiling

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Strenzke, F. (2012). Solutions for the Storage Problem of McEliece Public and Private Keys on Memory-Constrained Platforms. In: Gollmann, D., Freiling, F.C. (eds) Information Security. ISC 2012. Lecture Notes in Computer Science, vol 7483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33383-5_8

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  • DOI: https://doi.org/10.1007/978-3-642-33383-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33382-8

  • Online ISBN: 978-3-642-33383-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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