Table of Contents Author Guidelines Submit a Manuscript
Security and Communication Networks
Volume 2018, Article ID 2369507, 9 pages
https://doi.org/10.1155/2018/2369507
Research Article

Under Quantum Computer Attack: Is Rainbow a Replacement of RSA and Elliptic Curves on Hardware?

School of Computer Engineering, Shenzhen Polytechnic, Shenzhen 518055, China

Correspondence should be addressed to Haibo Yi; moc.621@iyobiah

Received 26 October 2017; Accepted 15 January 2018; Published 11 February 2018

Academic Editor: Umar M. Khokhar

Copyright © 2018 Haibo Yi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. Diffie, W. Diffie, and M. E. Hellman, “New Directions in Cryptography,” IEEE Transactions on Information Theory, vol. 22, no. 6, pp. 644–654, 1976. View at Publisher · View at Google Scholar · View at Scopus
  2. R. L. Rivest, A. Shamir, and L. Adleman, “A Method for Obtaining Digital Signatures and Public-Key Cryptosystems,” Communications of the ACM, vol. 26, no. 1, pp. 96–99, 1983. View at Publisher · View at Google Scholar · View at Scopus
  3. N. Koblitz, “Elliptic curve cryptosystems,” Mathematics of Computation, vol. 48, no. 177, pp. 203–209, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. V. S. Miller, “Use of elliptic curves in cryptography,” in Proceedings of the International Cryptology Conference (CRYPTO 85), 426, p. 417, Springer-Verlag, Berlin, Germany, 1985.
  5. G. D. Sutter, J.-P. Deschamps, and J. L. Imana, “Modular multiplication and exponentiation architectures for fast RSA cryptosystem based on digit serial computation,” IEEE Transactions on Industrial Electronics, vol. 58, no. 7, pp. 3101–3109, 2011. View at Publisher · View at Google Scholar · View at Scopus
  6. G. D. Sutter, J.-P. Deschamps, and J. L. Imana, “Efficient elliptic curve point multiplication using digit-serial binary field operations,” IEEE Transactions on Industrial Electronics, vol. 60, no. 1, pp. 217–225, 2013. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Cilardo, A. Mazzeo, L. Romano, and G. P. Saggese, “Exploring the design-space for FPGA-based implementation of RSA,” Microprocessors and Microsystems, vol. 28, no. 4, pp. 183–191, 2004. View at Publisher · View at Google Scholar · View at Scopus
  8. O. Nibouche, M. Nibouche, A. Bouridane, and A. Belatreche, “Fast architectures for FPGA-based implementation of RSA encryption algorithm,” in Proceedings of the IEEE International Conference on Field-Programmable Technology (FPT 2005), pp. 271–278, Washington, DC, USA, December 2004.
  9. Pund S. M., “Implementation of RSA algorithm using mersenne prime,” International Journal of Networking and Parallel Computing, vol. 1, pp. 33–41, 2014. View at Google Scholar
  10. Q. A. Al-Haija, M. Smadi, M. Al-Ja’fari, and A. Al-Shua’ibi, “Efficient FPGA implementation of RSA coprocessor using scalable modules,” in Proceedings of the International Symposium on Emerging Inter-networks, Communication and Mobility (EICM 2014), pp. 647–654, Elsevier, Amsterdam, Netherlands, 2014.
  11. K. C. C. Loi and S.-B. Ko, “High performance scalable elliptic curve cryptosystem processor for Koblitz curves,” Microprocessors and Microsystems, vol. 37, no. 4-5, pp. 394–406, 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Sakiyama, N. Mentens, L. Batina, B. Preneel, and I. Verbauwhede, “Reconfigurable modular arithmetic logic unit supporting high-performance RSA and ECC over GF(p),” International Journal of Electronics, vol. 94, no. 5, pp. 501–514, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. M. N. Hassan and M. Benaissa, “Small footprint implementations of scalable ECC point multiplication on FPGA,” in Proceedings of the 2010 IEEE International Conference on Communications, ICC 2010, pp. 1–4, Washington, DC, USA, May 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. M. Varchola, T. Güneysu, and O. Mischke, “MicroECC: A lightweight reconfigurable elliptic curve crypto-processor,” in Proceedings of the International Conference on Reconfigurable Computing and FPGAs (Reconfig 2011), pp. 204–210, Washington, DC, USA, 2013.
  15. P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM Journal on Computing, vol. 26, no. 5, pp. 1484–1509, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. J. Ding, J. E. Gower, and D. S. Schmidt, Multivariate Public Key Cryptosystems, Springer, Berlin, Germany, 2006.
  17. D. S. Johnson, “The NP-completeness column: an ongoing guide,” Journal of Algorithms, vol. 4, no. 1, pp. 87–100, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  18. A. Kipnis, J. Patarin, and L. Goubin, “Unbalanced oil and vinegar signature schemes,” in Proceedings of the Annual International Conference on the Theory and Applications of Cryptographic Techniques (Eurocrypt 99), vol. 1999, pp. 206–222, Springer, Berlin, Germany. View at Publisher · View at Google Scholar · View at Scopus
  19. J. Ding and D. Schmidt, “Rainbow, a new multivariable polynomial signature scheme,” in Proceedings of the International Conference on Applied Cryptography and Network Security (ACNS 2005), pp. 164–175, Springer, Berlin, Germany, 2005.
  20. A. Petzoldt, S. Bulygin, and J. Buchmann, “Selecting parameters for the rainbow signature scheme,” in Post-quantum cryptography, vol. 6061 of Lecture Notes in Comput. Sci., pp. 218–240, Springer, Berlin, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. B. Y. Yang and J. M. Chen, “Building secure tame-like multivariate public-key cryptosystems: the new TTS,” in Proceedings of the Australasian Conference on Information Security and Privacy (ACISP 2005), pp. 518–531, Springer, Berlin, Germany, 2005.
  22. E. Thomae and C. Wolf, “Cryptanalysis of enhanced TTS, STS and all its variants, or: why cross-terms are important,” in Proceedings of the International Conference on Cryptology in Africa (Africacrypt 2012), pp. 188–202, Springer, Berlin, Germany, 2012.
  23. T. Matsumoto and H. Imai, “Public quadratic polynomial-tuples for efficient signature-verification and message-encryption,” in Proceedings of the Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 88), pp. 419–453, Springer, Berlin, Germany, 1988.
  24. E. Thomae and C. Wolf, “Solving underdetermined systems of multivariate quadratic equations revisited,” in Proceedings of the International Conference on Practice and Theory of Public-Key Cryptography (PKC 2012), 171, pp. Berlin, Germany–156, Springer, 2012.
  25. T. Moh, “A public key system with signature and master key functions,” Communications in Algebra, vol. 27, no. 5, pp. 2207–2222, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. A. Bogdanov, T. Eisenbarth, A. Rupp et al., “Time-area optimized public-key engines: MQ-cryptosystems as replacement for elliptic curves?” in Proceedings of the Conference on Cryptographic Hardware and Embedded Systems (CHES 2008), pp. 45–61, Springer, Berlin, Germany, 2008.
  27. H. Yi and S. Tang, “Very small FPGA processor for multivariate signatures,” The Computer Journal, vol. 59, no. 7, pp. 1091–1101, 2016. View at Publisher · View at Google Scholar · View at Scopus
  28. S. Tang, H. Yi, J. Ding, H. Chen, and G. Chen, “High-speed hardware implementation of rainbow signature on FPGAs,” in Proceedings of the International Workshop on Post-Quantum Cryptography (PQCrypto 2011), pp. 228–243, Springer, Berlin, Germany, 2011.
  29. B. Yang, C. Cheng, B. Chen, and J. Chen, “Implementing minimized multivariate PKC on low-resource embedded systems,” in Proceedings of the Security in Pervasive Computing, 3rd International Conference (SPC 2006), vol. 3934, pp. 73–88, Springer, Berlin, Germany, 2006.
  30. H. Yi, S. Tang, and R. Vemuri, “Fast inversions in small finite fields by using binary trees,” The Computer Journal, vol. 59, no. 7, pp. 1102–1112, 2016. View at Publisher · View at Google Scholar · View at Scopus
  31. P. C. Kocher, “Timing attacks on implementations of diffie-hellman, RSA, DSS, and other systems,” in Proceedings of the International Cryptology Conference on Advances in Cryptology (CRYPTO 96), pp. 104–113, Springer, Berlin, Germany, 1996.
  32. P. C. Kocher, J. Jaffe, and B. Jun, “Differential power analysis,” in Proceedings of the International Cryptology Conference on Advances in Cryptology (CRYPTO 99), pp. 388–397, Springer, Berlin , Germany, 1999.
  33. J. J. Quisquater and D. Samyde, “ElectroMagnetic analysis: measures and countermeasures for smart cards,” in Proceedings of the International Conference on Research in Smart Cards (E-Smart 2001), pp. 200–210, Springer, Berlin, Germany, 2001.
  34. S. P. Skorobogatov and R. J. Anderson, “Optical fault induction attacks,” in Proceedings of the Conference on Cryptographic Hardware and Embedded Systems (CHES 2002), pp. 2–12, Springer, Berlin, Germany, 2003.
  35. D. Genkin, A. Shamir, and E. Tromer, “RSA key extraction via low-bandwidth acoustic cryptanalysis,” in Proceedings of the International Cryptology Conference (CRYPTO 2014), pp. 17–21, Springer, Berlin, Germany, 2014.
  36. S. Skorobogatov, “Data remanence in flash memory devices,” in Proceedings of the Conference on Cryptographic Hardware and Embedded Systems (CHES 2005), pp. 339–353, Springer, Berlin, Germany, 2005.
  37. D.-H. Kim, P. J. Nair, and M. K. Qureshi, “Architectural support for mitigating row hammering in DRAM memories,” Computer Architecture Letters, vol. 14, pp. 9–12, 2015. View at Google Scholar
  38. M. Joye, A. K. Lenstra, and J.-J. Quisquater, “Chinese remaindering based cryptosystems in the presence of faults,” Journal of Cryptology, vol. 12, no. 4, pp. 241–245, 1999. View at Publisher · View at Google Scholar · View at Scopus
  39. D. M. D. Boneh and R. J. Lipton, “On the importance of eliminating errors in cryptographic computations,” Journal of Cryptology, vol. 14, pp. 101–119, 1999. View at Google Scholar
  40. Y. Hashimoto, T. Takagi, and K. Sakurai, “General fault attacks on multivariate public key cryptosystems,” in Post-quantum cryptography, vol. 7071 of Lecture Notes in Comput. Sci., pp. 1–18, Springer, Heidelberg, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  41. R. Mayer-Sommer, “Smartly analyzing the simplicity and the power of simple power analysis on smartcards,” in Proceedings of the Conference on Cryptographic Hardware and Embedded Systems (CHES 2000), pp. 78–92, pringer, Berlin, Germany, 2000.
  42. K. Okeya, T. Takagi, and C. Vuillaume, “On the importance of protecting δ in SFLASH against side channel attacks,” in Proceedings of the International Conference on Coding and Computing (ITCC 2004), pp. 560–568, Washington, DC, USA, 2004. View at Scopus
  43. H. Yi and W. Li, “On the Importance of Checking Multivariate Public Key Cryptography for Side-Channel Attacks: The Case of enTTS Scheme,” The Computer Journal, pp. 1–13, 2017. View at Google Scholar