부호 기반 McEliece 암호 체계와 안전성 분석

  • 발행 : 2015.05.29

초록

오류 정정 부호(error-correcting code)를 사용하는 McEliece 암호 체계는 양자 컴퓨터에서도 안전한 공개키 암호기법으로서 주목 받아왔다. 본고에서는 McEliece 암호 체계에 사용되는 오류 정정 부호와 그 조건, 암호 체계의 구조와 그 발전 과정 및 응용을 알아보고, 안전성 분석에 대해 소개한다.

키워드

참고문헌

  1. Al Jabri A. Kh. "A statistical Decoding Algorithm for General Linear Blockl Codes," IMA Int. Conf., volume 2260 of Lecture Notes in Computer Science, Springer (2001), pp. 1-8.
  2. Avanzi R., Hoerder S., Page D., and Tunstall M. "Side-Channel Attacks on the McEliece and Niederreiter Public-Key Cryptosystems," Journal of Cryptographic Engineering 1(4) (2011), pp. 271-281. https://doi.org/10.1007/s13389-011-0024-9
  3. Berger T. P., Cayrel P., Gaborit P., and Otmani A. "Reducing Key Length of the McEliece Cryptosystem," AFRICACRYPT, volume 5580 of Lecture Notes in Computer Science, Springer (2009), pp. 77-97.
  4. Bernstein D. J., Lange T., and Peters C. "Attacking and defending the McEliece cryptosystem," PQCrypto, volume 5299 of Lecture Notes in Computer Science, Springer (2008), pp. 31-46.
  5. Bernstein D. J. "Grover vs McEliece," PQCrypto, volume 6061 of Lecture Notes in Computer Science, Springer (2010), pp. 73-80.
  6. Bernstein D. J., Lange T., and Peters C. "Wild McEliece," Selected Areas in Cryptography, volume 6544 of Lecture Notes in Computer Science, Springer (2010), pp. 143-158.
  7. Bernstein D. J., Lange T., and Peters C. "Wild McEliece Incognito," PQCrypto, volume 7071 of Lecture Notes in Computer Science, Springer (2011), pp. 244-254.
  8. Bernstein D. J., Lange T., and Peters C. "Smaller decoding exponents: ball-collision decoding," CRYPTO, LNCS vol 6841 (2011), pp.743-760.
  9. Berson T. A. "Failure of the McEliece Public-Key Cryptosystem Under Message-Resend and Related-Message Attack," CRYPTO, volume 1294 of Lecture Notes in Computer Science, Springer (1997), pp. 213-220.
  10. Brickell E. F., and Odlyzko A. M. "Cryptanalysis: A survey of recent results," Proc. of IEEE '88, vol. 75, pp578-593.
  11. Canteaut A., and Chabaud F. "A new algorithm for Finding Minimum-Weight Words in a Linear Code: Application to McEliece's Cryptosystem and to narrow-sense BCH codes of length 511," IEEE Transactions on Information Theory, 44(1) (1998), pp. 367-378. https://doi.org/10.1109/18.651067
  12. Courtois N., Finiasz M., and Sendrier N. "How to achieve a McEliece-based Digital Signature Scheme", ASIACRYPT, volume 2248 of Lecture Notes in Computer Science, Springer (2001), pp. 157-174.
  13. Engelbert D., Overbeck R., and Schmidt A. "A Summary of McEliece-Type Cryptosystems and their Security," Journal of Mathematical Cryptology 1(2) (2007), pp. 151-199. https://doi.org/10.1515/JMC.2007.009
  14. Faugere J., Otmani A., Perret L., Portzamparc F., and Tillich J. "Structural Cryptanalysis of McEliece Schemes with Compact Keys," Cryptology ePrint Archive, (2014), Report 2014/210.(http://eprint.iacr.org/).
  15. Faure C., and Minder L. "Cryptanalysis of the McEliece cryptosystem over hyperelliptic curves," Proceedings of the eleventh International Workshop on Algebraic and Combinatorial Coding Theory (2008), pp. 99-107.
  16. Finiasz M., and Sendrier N. "Digital Signature Scheme Based on McEliece," Encyclopedia of Cryptography and Security (2011), pp. 342-343.
  17. Fujisaki E., and Okamoto T. "Secure Integration of Asymmetric and Symmetric Encryption Schemes," CRYPTO, volume 1666 of Lecture Notes in Computer Science, Springer (1999), pp. 537-554.
  18. Fujita H. "Quantum McEliece public-key cryptosystem," Quantum Information & Computation 12(3-4) (2012), pp. 181-202.
  19. Goborit P. "Shorter keys for code based cryptography," Proceedings of WCC 2005 (2005), pp. 81-91.
  20. Howgrave-Graham N., and Joux A. "New Generic Algorithms for Hard Knapsacks," EUROCRYPT, volume 6110 of Lecture Notes in Computer Science, Springer (2010), pp. 235-256.
  21. Kobara K., and Imai H. "Semantically Secure McEliece Public-Key Cryptosystems-Conversions for McEliece PKC," Public Key Cryptography, volume 1992 of Lecture Notes in Computer Science, Springer (2001), pp. 19-35.
  22. Kobara K., and Imai H. "On the one-wayness against chosen-plaintext attacks of the Loidreau's modified McEliece PKC," IEEE Transactions on Information Theory 49(12) (2003), pp. 3160-3168. https://doi.org/10.1109/TIT.2003.820016
  23. Lee P. J., and Brickell E. F. "An Observation on the security of McEliece's Public-Key Cryptosystem," EUROCRYPT, Lec Notes in CS (1988), pp. 275-280.
  24. Li Y., Deng R. H., and Wang X. "On the equivalence of McEliece's and Niederreiter's public-key cryptosystems," IEEE Transactions on Information Theory 40(1) (1994) pp. 271-273. https://doi.org/10.1109/18.272496
  25. Loidreau P. "Strengthening McEliece cryptosystem," ASIACRYPT, volume 1976 of Lecture Notes in Computer Science, Springer (2000), pp. 585-598.
  26. May A., Meurer A., and Thomae E. "Decoding Random Linear Codes in O(20.054n)," ASIACRYPT, volume 7073 of Lecture Notes in Computer Science, Springer (2011), pp. 107-124.
  27. McEliece R. J. "A Public Key Cryptosystem based on Algebraic Coding Theory," DSN progress report 42-44 (1978), pp. 114-116.
  28. Misoczki R., Tillich J., Sendrier N., and Barreto P. S. L. M. "MDPC-McEliece: New McEliece variants from Moderate Density Parity-Check codes," Proceedings of the 2013 IEEE International Symposium on Information Theory, IEEE (2013), pp. 2069-2073.
  29. Overbeck R., and Sendrier N. "Code-based cryptography," Post-Quantum Cryptography, Springer (2009), pp. 95-145.
  30. 박승안, "선형 부호," 부호이론, 京文社 (2005), pp. 207-306.
  31. Peters C. "Information-Set Decoding for Linear Codes over Fq," PQCrypto, volume 6061 of Lecture Notes in Computer Science, Springer (2010), pp. 81-94.
  32. Persichetti E. "Compact McEliece keys based on Quasi-Dyadic Srivastava codes," Journal of Mathematical Cryptology 6(2) (2012), pp. 149-169.
  33. Pless V. "Introduction to the Theory of Error-Correcting Codes," John Wiley & Sons (1998), pp.1-38.
  34. Pointcheval D. "Chosen-Ciphertext Security for Any One-Way Cryptosystem," Public Key Cryptography, volume 1751 of Lecture Notes in Computer Science, Springer (2000), pp. 129-146.
  35. Sendrier N. "On the security of the McEliece pk cryptosystem," M. Blaum, P. Farrel, and H. van Tilborg, editors, Proceedings of Workshop honoring Prof. Bob McEliece on his 60th birthday (2002), pp. 141-163.
  36. Shor P. W. "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer," SIAM Journal on Computing 26(5) (1997), pp. 1484-1509. https://doi.org/10.1137/S0097539795293172
  37. Sidelnikov V.M., and Shestakov S.O. "On insecurity of cryptosystems based on generalized Reed-Solomon codes," Discrete Mathematics and Applications, 1(4) (1992), pp. 439-444.
  38. Stern J. "A method for finding codewords of small weight," Proceedings of Coding Theory and Applications (1989), pp. 106-113.
  39. Strenzke F. "Timing Attacks against the Syndrome Inversion in Code-Based Cryptosystems," Post-Quantum Cryptography, LNCS vol 7932 (2013), pp. 217-230.
  40. Sugiyama Y., Kasahara M., Hirasawa S., and Namekawa T. "aFurther results on Goppa codes and their applications to constructing efficient binary codes," IEEE Transactions on Information Theory 22(5) (1976), pp. 518-526. https://doi.org/10.1109/TIT.1976.1055610
  41. Zajac P. "A note on CCA2-protected McEliece cryptosystem with a systematic public key," Cryptology ePrint Archive, (2014), Report 2014/651.(http://eprint.iacr.org/).