The Journal of Supercomputing

, Volume 71, Issue 5, pp 1803–1816 | Cite as

A parallel algorithm for secure multicast

  • J. A. Álvarez-Bermejo
  • J. M. Arrufat
  • J. A. López-Ramos


In this work, we introduce algorithms to speedup and to scale a classical secure multicast protocol that currently goes unused due to its computational and data management requirements when the audience becomes large. This is in spite of its agreeable cryptographic properties, which offers real applicability. A core component of such an algorithm is the well-known method to solve congruent systems, the Chinese remainder algorithm (CRA). This work presents the study, design and implementation of a software approach to the CRA on different parallel architectures. Special attention is placed on big integers, which affect method performance, given that the system is more secure as the modules become larger. This problem leads to the design of a new and more efficient method to address these issues in a scalable way. The results represent an enhancement in efficiency, performance and scalability when compared to existing alternatives.


Cryptography Secure multicast Parallel algorithms  Chinese remainder algorithm 


  1. 1.
    Lin KY, Krishna B, Krishna H (1994) Rings, fields, the Chinese remainder algorithm and an extension—Part I: theory. IEEE Trans Circuits Syst II Analog Digital Signal Process 41(10):641–655Google Scholar
  2. 2.
    Rosen KH (2011) Discrete mathematics and its applications, 7th edn. McGraw-Hill Higher Education. isbn: 978-0077431440Google Scholar
  3. 3.
    Wang Y (1998) New Chinese remainder algorithms. Conference record of the thirty-second asilomar conference on signals, systems and computers, vol 1. pp 165–171Google Scholar
  4. 4.
    Toyoshima H, Satoh K, Ariyama K (1996) High-speed hardware algorithms for Chinese remainder theorem. 1996 IEEE International Symposium on circuits and systems, ISCAS 96, connecting the World, vol 2. pp 265–268Google Scholar
  5. 5.
    Lai YP, Chang CC (2003) Parallel computational algorithms for generalized Chinese remainder theorem. Comput Electr Eng 29:801–811CrossRefMATHGoogle Scholar
  6. 6.
    Olagunju AO (2008) A computational exploration of the Chinese remainder theorem. J Appl Math Inf 26:307–316Google Scholar
  7. 7.
    Chang CC, Kuo Y T, Lai YP (2006) Parallel computation of residue number system. International Conference on computing and informatics, ICOCI 2006. pp 1–6Google Scholar
  8. 8.
    Zhu S, Jajodia S (2010) Scalable group key management for secure multicast: A taxonomy and new directions. In: Huang H, MacCallum D, Du D-Z (eds) Network security. Springer, Berlin, pp 57–75Google Scholar
  9. 9.
    Liu B, Zhang W, Jiang T (2004) A scalable key distribution scheme for conditional access system in digital pay-TV system. IEEE Consum Electron 50(2):632–637CrossRefGoogle Scholar
  10. 10.
    Chiou G, Chen W (1989) Secure broadcasting using the secure lock. IEEE Trans Softw Eng 15(8):929–934CrossRefGoogle Scholar
  11. 11.
    Kruus S, Macker JP (1998) Techniques and issues in multicast security. In: Proceedings of military communications conference, MILCOM. pp 1028–1032Google Scholar
  12. 12.
    Lin KY, Krishna B, Krishna H (1994) Rings, fields, the Chinese remainder theorem and an extension—Part II: applications to digital signal processing. IEEE Trans Circuits Syst II Analog Digital Signal Process 41:656–668CrossRefMATHGoogle Scholar
  13. 13.
    Li Y, Xiao L, Wang Z, Tian H (2011) High performance point-multiplication for conic curves cryptosystem based on standard NAF algorithm and Chinese remainder theorem. 2011 International Conference on information science and applications (ICISA), pp 1–8Google Scholar
  14. 14.
    Rabin MO (1980) Rabin probabilistic algorithm for testing primality. J Number Theory 2:128–138CrossRefMathSciNetGoogle Scholar
  15. 15.
    Antequera N, Lopez-Ramos JA (2011) Remarks and countermeasures on a cryptoanalysis of a secure multicast protocol. In: Proceedings of 7th international conference on next generation web services practices, Salamanca 2011. pp 201–205Google Scholar
  16. 16.
    Zhu S, Jajodia S (2010) Scalable group key management for securemulticast: a taxonomy and new directions. In: Network security. pp 57–75Google Scholar
  17. 17.
    Chen H (2009) CRT-based high-speed parallel architecture for long BCH encoding. IEEE Trans Circuits Systems II Express Briefs 56(8):684–686CrossRefGoogle Scholar
  18. 18.
    Toyoshima H, Satoh K, Ariyama K (1996) High-speed hardware algorithms for Chinese remainder theorem. In: 1996 IEEE international symposium on circuits and systems, vol 2. ISCAS ’96, Connecting the World. pp 265–268Google Scholar
  19. 19.
    Barnat J, Bauch P, Brim L, Ceska M (2010) Employing multiple CUDA devices to accelerate LTL model checking. 2010 IEEE 16th international conference on parallel and distributed systems(ICPADS), pp 259–266Google Scholar
  20. 20.
    Karunadasa NP (2009) Accelerating high performance applications with CUDA and MPI. In: 2009 International conference on industrial and informations system (ICIIS). pp 331–336Google Scholar
  21. 21.
    Manavski SA (2007) CUDA compatible GPU as an efficient hardware accelerator for AES cryptography. In: Signal Processing and Communications, ICSPC 2007. pp 65–68Google Scholar
  22. 22.
    Zhao Y, Huang Z, Chen B, Fang Y, Yan M, Yang Z (2010) Local acceleration in distributed geographic information processing with CUDA. 18th international conference on geoinformatics. pp 1–6Google Scholar
  23. 23.
    Chakrabarti G et al (2012) CUDA: compiling and optimizing for a GPU platform. Procedia Comput 9:1910–1919CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • J. A. Álvarez-Bermejo
    • 1
  • J. M. Arrufat
    • 2
  • J. A. López-Ramos
    • 3
  1. 1.Department of InformaticsUniversity of Almeria (Spain)AlmeriaSpain
  2. 2.Corporate and investment bankingManagement Solutions corp.MadridSpain
  3. 3.Department of MathematicsUniversity of Almeria (Spain)AlmeriaSpain

Personalised recommendations