KSII Transactions on Internet and Information Systems (TIIS)

  • 제11권6호
  • /
  • Pages.3166-3187
  • /
  • 2017
  • /
  • 1976-7277(pISSN)
  • /
  • 1976-7277(eISSN)
한국인터넷정보학회 (Korean Society for Internet Information)
권호 표지
DOI QR코드

DOI QR Code

HS-Sign: A Security Enhanced UOV Signature Scheme Based on Hyper-Sphere

  • Chen, Jiahui (School of Computer Science & Engineering,South China University of Technology) ;
  • Tang, Shaohua (School of Computer Science & Engineering,South China University of Technology) ;
  • Zhang, Xinglin (School of Computer Science & Engineering,South China University of Technology)
  • 투고 : 2016.12.07
  • 심사 : 2017.03.29
  • 발행 : 2017.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

For "generic" multivariate public key cryptography (MPKC) systems, experts believe that the Unbalanced Oil-Vinegar (UOV) scheme is a feasible signature scheme with good efficiency and acceptable security. In this paper, we address two problems that are to find inversion solution of quadratic multivariate equations and find another structure with some random Oil-Oil terms for UOV, then propose a novel signature scheme based on hyper-sphere (HS-Sign for short) which directly answers these two problems. HS-Sign is characterized by its adding Oil-Oil terms and more advantages compared to UOV. On the one side, HS-Sign is based on a new inversion algorithm from hyper-sphere over finite field, and is shown to be a more secure UOV-like scheme. More precisely, according to the security analysis, HS-Sign achieves higher security level, so that it has larger security parameters choice ranges. On the other side, HS-Sign is beneficial from both the key side and computing complexity under the same security level compared to many baseline schemes. To further support our view, we have implemented 5 different attack experiments for the security analysis and we make comparison of our new scheme and the baseline schemes with simulation programs so as to show the efficiencies. The results show that HS-Sign has exponential attack complexity and HS-Sign is competitive with other signature schemes in terms of the length of the message, length of the signature, size of the public key, size of the secret key, signing time and verification time.

키워드

참고문헌

  1. Jintai Ding and Bo-Yin Yang, "Multivariate public key cryptography," in Proc. of Daniel J. Bernstein, Johannes Buchmann, and Erik Dahmen, editors, Post-Quantum Cryptography, pp. 193-241, Springer Berlin Heidelberg, 2009.
  2. Koichi Sakumoto, Taizo Shirai, and Harunaga Hiwatari, "Public-key identification schemes based on multivariate quadratic polynomials," in Proc. of Phillip Rogaway, editor, Advances in Cryptology -CRYPTO 2011, volume 6841 of Lecture Notes in Computer Science, pp. 706-723, Springer Berlin Heidelberg, 2011.
  3. Michael R Garey and David S Johnson, "Computer and intractability, A Guide to the theory of NP-Completeness," Ney York, NY: WH Freeman and Company, 1979.
  4. Jacques Patarin and Louis Goubin, "Trapdoor one-way permutations and multivariate polynomials," Information and Communications Security, pp. 356-368, 1997.
  5. Albrecht Petzoldt, Stanislav Bulygin, and Johannes Buchmann, "CyclicRainbow - A multivariate signature scheme with a partially cyclic public key," in Proc. of SCC, pp. 229-235, 2010.
  6. Aviad Kipnis, Jacques Patarin, and Louis Goubin, "Unbalanced Oil and Vinegar signature schemes, " in Proc. of Jacques Stern, editor, Advances in Cryptology -EUROCRYPT'99, volume 1592 of Lecture Notes in Computer Science, pp. 206-222, Springer Berlin Heidelberg, 1999.
  7. Jintai Ding, Jason E Gower, and Dieter S Schmidt, "Multivariate public key cryptosystems," volume 25. Springer, 2006.
  8. Jacques Patarin, "Hidden fields equations (HFE) and isomorphisms of polynomials (IP): two new families of asymmetric algorithms, " in Proc. of Advances in Cryptology -EUROCRYPT '96, International Conference on the Theory and Application of Cryptographic Techniques, Saragossa, Spain, pp. 33-48, May 12-16, 1996.
  9. Tsutomu Matsumoto and Hideki Imai, "Public quadratic polynomial-tuples for efficient signature-verification and message-encryption, " in Proc. of D. Barstow, W. Brauer, P. Brinch Hansen, D. Gries, D. Luckham, C. Moler, A. Pnueli, G. Seegmuller, J. Stoer, N. Wirth, and ChristophG. Gunther, editors, Advances in Cryptology -EUROCRYPT '98, volume 330 of Lecture Notes in Computer Science, pp. 419-453, Springer Berlin Heidelberg, 1988.
  10. Christopher Wolf, An Braeken, and Bart Preneel, "On the security of stepwise triangular systems," Designs, Codes and Cryptography, 40(3):285-302, 2006. https://doi.org/10.1007/s10623-006-0015-5
  11. Mehdi-Laurent Akkar, Nicolas Courtois, Romain Duteuil, and Louis Goubin, "A fast and secure implementation of sflash, " in Proc. of Public Key Cryptography - PKC 2003, 6th International Workshop on Theory and Practice in Public Key Cryptography, Miami, FL, USA, pp. 267-278, January 6-8, 2003.
  12. Jacques Patarin, Louis Goubin, and Nicolas Courtois, "C*-+and HM: variations around two schemes of t. matsumoto and h. imai, " in Proc. of Advances in Cryptology - ASIACRYPT '98, International Conference on the Theory and Applications of Cryptology and Information Security, Beijing, China, pp. 35-49, October 18-22, 1998.
  13. Jintai Ding, "A new variant of the matsumoto-imai cryptosystem through perturbation," in Proc. of Public Key Cryptography - PKC 2004, 7th International Workshop on Theory and Practice in Public Key Cryptography, Singapore, pp. 305-318, March 1-4, 2004.
  14. Jintai Ding and Jason E. Gower, "Inoculating multivariate schemes against differential attacks, " in Proc. of Public Key Cryptography - PKC 2006, 9th International Conference on Theory and Practice of Public-Key Cryptography, New York, NY, USA, pp. 290-301, April 24-26, 2006.
  15. Jacques Patarin, "Hidden fields equations (HFE) and isomorphisms of polynomials (IP): Two new families of asymmetric algorithms," in Proc. of Ueli Maurer, editor, Advances in Cryptology EUROCRYPT 96, volume 1070 of Lecture Notes in Computer Science, pp. 33-48, Springer Berlin Heidelberg, 1996.
  16. Jintai Ding and Dieter Schmidt, "Cryptanalysis of hfev and internal perturbation of HFE, " in Proc. of Public Key Cryptography - PKC 2005, 8th International Workshop on Theory and Practice in Public Key Cryptography, Les Diablerets, Switzerland, pp. 288-301, January 23-26, 2005.
  17. Jacques Patarin, Nicolas Courtois, and Louis Goubin, "Quartz, 128-bit long digital signatures, " in Proc. of Topics in Cryptology - CT-RSA 2001, The Cryptographer's Track at RSA Conference 2001, San Francisco, CA, USA, pp. 282-297, April 8-12, 2001.
  18. Yun-Ju Huang, Feng-Hao Liu, and Bo-Yin Yang, "Public-key cryptography from new multivariate quadratic assumptions, " in Proc. of Public Key Cryptography - PKC 2012 -15th International Conference on Practice and Theory in Public Key Cryptography,Darmstadt, Germany, pp. 190-205, May 21-23, 2012.
  19. Takanori Yasuda, Tsuyoshi Takagi, and Kouichi Sakurai, "Multivariate signature scheme using quadratic forms, " in Proc. of Post-Quantum Cryptography - 5th International Workshop, PQCrypto 2013, Limoges, France, pp. 243-258, June 4-7, 2013.
  20. Chengdong Tao, Adama Diene, Shaohua Tang, and Jintai Ding, "Simple matrix scheme for encryption," in Proc. of Post-Quantum Cryptography - 5th International Workshop, PQCrypto 2013, Limoges, France, pp. 231-242, June 4-7, 2013.
  21. Takanori Yasuda, Jintai Ding, Tsuyoshi Takagi, and Kouichi Sakurai, "A variant of rainbow with shorter secret key and faster signature generation, " in Proc. of the first ACM workshop on Asia public-key cryptography, AsiaPKC'13, Hangzhou, China, pp. 57-62, May 8, 2013.
  22. Takanori Yasuda, Tsuyoshi Takagi, and Kouichi Sakurai, "Efficient variant of rainbow using sparse secret keys," JoWUA, vol. 5, no. 3, pp. 3-13, 2014.
  23. Jintai Ding, Albrecht Petzoldt, and Lih-chung Wang, "The cubic simple matrix encryption scheme," in Proc. of Post-Quantum Cryptography - 6th International Workshop, PQCrypto 2014, Waterloo, ON, Canada, pp. 76-87, October 1-3, 2014.
  24. Jaiberth Porras, John Baena, and Jintai Ding, "ZHFE, a new multivariate public key encryption scheme," in Proc. of Post-Quantum Cryptography - 6th International Workshop,PQCrypto 2014, Waterloo, ON, Canada, pp. 229-245, October 1-3, 2014.
  25. Wuqiang Shen and Shaohua Tang, "RGB, a mixed multivariate signature scheme," Comput. J., vol. 59, no. 4, pp. 439-451, 2016. https://doi.org/10.1093/comjnl/bxv056
  26. Alan Szepieniec, Jintai Ding, and Bart Preneel, "Extension field cancellation: A new central trapdoor for multivariate quadratic systems," in Proc. of Post-Quantum Cryptography - 7th International Workshop, PQCrypto 2016, Fukuoka, Japan, pp. 182-196, February 24-26, 2016.
  27. Albrecht Petzoldt, Stanislav Bulygin, and Johannes A. Buchmann, "A multivariate based threshold ring signature scheme," Appl. Algebra Eng. Commun. Comput, 24(3-4):255-275, 2013. https://doi.org/10.1007/s00200-013-0190-3
  28. Shaohua Tang and Lingling Xu, "Towards provably secure proxy signature scheme based on isomorphisms of polynomials," Future Generation Computer Systems, 30(0):91 - 97, 2014. https://doi.org/10.1016/j.future.2013.06.003
  29. Jiahui Chen, Shaohua Tang, Daojing He, and Yang Tan, "Online/offline signature based on uov in wireless sensor networks," Wireless Networks, pp. 1-12, 2016.
  30. Jacques Patarin, "The oil and vinegar signature scheme," in Proc. of Dagstuhl Workshop on Cryptography, volume 80, 1997.
  31. Aviad Kipnis and Adi Shamir, "Cryptanalysis of the Oil and Vinegar signature scheme, " in Proc. of Hugo Krawczyk, editor, Advances in Cryptology -CRYPTO '98, volume 1462 of Lecture Notes in Computer Science, pp. 257-266, Springer Berlin Heidelberg, 1998.
  32. Shaohua Tang, Lingling Xu, Niu Liu, Xinyi Huang, Jintai Ding, and Zhiming Yang, "Provably secure group key management approach based upon hyper-sphere," Parallel and Distributed Systems, IEEE Transactions on, PP(99):1-11, 2014.
  33. W. Cao, L. Hu, J. Ding, and Z. Yin, "Kipnis-shamir attack on unbalanced oil-vinegar scheme," Information Security Practice and Experience, pages 168-180, 2011.
  34. Wieb Bosma, John Cannon, and Catherine Playoust, "The Magma algebra system I: The user language," Journal of Symbolic Computation, 24(3-4):235 - 265, 1997. https://doi.org/10.1006/jsco.1996.0125
  35. Jean-Charles Faugere, "A new efficient algorithm for computing Grobner bases (F4)," Journal of Pure and Applied Algebra, 139:61-88, 1999. https://doi.org/10.1016/S0022-4049(99)00005-5
  36. Charles Bouillaguet, Hsieh-Chung Chen, Chen-Mou Cheng, Tung Chou, Ruben Niederhagen, Adi Shamir, and Bo-Yin Yang, "Fast exhaustive search for polynomial systems in F2," in Proc. of Stefan Mangard and Franois-Xavier Standaert, editors, Cryptographic Hardware and Embedded Systems, CHES 2010, volume 6225 of Lecture Notes in Computer Science, pages 203-218, Springer Berlin Heidelberg, 2010.
  37. Magali Bardet, Jean-Charles Faugere, and Bruno Salvy, "On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations," in Proc. of Intl Conference on Polynomial System Solving, pages 71-74, 2004.
  38. Jintai Ding, Bo-Yin Yang, Chia-Hsin Owen Chen, Ming-Shing Chen, and Chen-Mou Cheng, "New differential-algebraic attacks and reparametrization of rainbow," in Proc. of Applied Cryptography and Network Security, 6th International Conference, ACNS 2008, New York, NY, USA, June 3-6, Proceedings, pages 242-257, 2008.
  39. Luk Bettale, Jean-Charles Faugere, and Ludovic Perret, "Hybrid approach for solving multivariate systems over finite fields," J. Mathematical Cryptology, 3(3):177-197, 2009. https://doi.org/10.1515/JMC.2009.009
  40. Enrico Thomae and Christopher Wolf, "Cryptanalysis of enhanced tts, STS and all its variants, or: Why cross-terms are important," in Proc. of Progress in Cryptology - AFRICACRYPT 2012 - 5th International Conference on Cryptology in Africa, Ifrance, Morocco, July 10-12, Proceedings, pages 188-202, 2012.
  41. Jacques Patarin, "Cryptanalysis of the matsumoto and imai public key scheme of eurocrypt'88, " in Proc. of Advances in Cryptology - CRYPTO '95, 15th Annual International Cryptology Conference, Santa Barbara, California, USA, August 27-31, 1995, Proceedings, pages 248-261, 1995.
  42. Jintai Ding, Lei Hu, Xuyun Nie, Jianyu Li, and John Wagner, "High order linearization equation (HOLE) attack on multivariate public key cryptosystems," in Proc. of Public Key Cryptography - PKC 2007, 10th International Conference on Practice and Theory in Public-Key Cryptography, Beijing, China, April 16-20, 2007, Proceedings, pages 233-248, 2007.
  43. Albrecht Petzoldt, Ming-Shing Chen, Bo-Yin Yang, Chengdong Tao, and Jintai Ding, "Design principles for hfev- based multivariate signature schemes," in Proc. of Advances in Cryptology - ASIACRYPT 2015 - 21st International Conference on the Theory and Application of Cryptology and Information Security, Auckland, New Zealand, November 29 - December 3, Proceedings, Part I, pages 311-334, 2015.
  44. Jintai Ding and Dieter Schmidt, "Rainbow, a new multivariable polynomial signature scheme, " in Proc. of Applied Cryptography and Network Security, Third International Conference, ACNS 2005, New York, NY, USA, June 7-10, Proceedings, pages 164-175, 2005.
  45. Jean-Charles Faugère and Antoine Joux, "Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using gröbner bases," in Proc. of Advances in Cryptology -CRYPTO 2003, 23rd Annual International Cryptology Conference, Santa Barbara, California, USA, August 17-21, Proceedings, pages 44-60, 2003.
  46. Ronald L. Rivest, Adi Shamir, and Leonard M. Adleman, "A method for obtaining digital signatures and public-key cryptosystems," Commun. ACM, 21(2):120-126, 1978. https://doi.org/10.1145/359340.359342
  47. Don Johnson, Alfred Menezes, and Scott A. Vanstone, "The elliptic curve digital signature algorithm (ECDSA)," Int. J. Inf. Sec., 1(1):36-63, 2001. https://doi.org/10.1007/s102070100002