Skip to main content

A New Common Subexpression Elimination Algorithm for Constant Matrix Multiplications Over Binary Field

  • Conference paper
  • First Online:
Transactions on Engineering Technologies

Abstract

In this work, a new multi-term common subexpression elimination (CSE) algorithm is proposed. The new algorithm aims to reduce area-delay-production (ADP) in VLSI designs of constant matrix multiplication (CMM) over binary field. For promoting delays optimization, a gate-level delay computing method is used to compute the delays based on the transformed constant matrices. The new algorithm also takes a greedy algorithm to search the minimal ADP result. The worst case computational complexities of the delay computing method and the new CSE algorithm are analyzed, respectively. Experimental results have shown that the new CSE algorithm has more efficient in ADP reduction in VLSI designs of binary CMM.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. N. Chen, Z.Y. Yan, Cyclotomic FFTs with reduced additive complexities based on a novel common subexpression elimination algorithm. IEEE Trans. Signal Process. 57(3), 1010–1020 (2009)

    Article  MathSciNet  Google Scholar 

  2. A. Chandrakasan, M. Potkonjak, R. Mehra, J. Rabaey, R.W. Brodersen, Optimizing power using transformations. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 14(1), 12–31 (1995)

    Google Scholar 

  3. N. Wu, X.Q. Zhang, Y.F. Ye, L.D. Lan, in Proceedings of The World Congress on Engineering and Computer Science 2013, WCECS 2013. Improving common subexpression elimination algorithm with a new gate-level delay computing method. Lecture Notes in Engineering and Computer Science, 23–25 October. (San Francisco, USA, 2013), pp. 677–682

    Google Scholar 

  4. O. Gustafsson, M. Olofsson, in First International Workshop on Arithmetic of Finite Fields (WAIFI 2007). Complexity reduction of constant matrix computations over the binary field, LNCS, vol. 4547 (Springer, 2007), pp. 103–115

    Google Scholar 

  5. R. Paško, P. Schaumont, V. Derudder, S. Vernalde, D. Ďuračková, A new algorithm for elimination of common subexpressions. IEEE Trans. Comput.-Aided Design 18(1), 58–68 (1999)

    Article  Google Scholar 

  6. C. Zeng, N. Wu, X.Q. Zhang, The optimization of AES S-box circuit design based on multiple-term CSE algorithm. Acta Electronica Sinica (Chinese Edition), 42(3), (2014)

    Google Scholar 

  7. X. Zhang, K.K. Parhi, On the optimum constructions of composite field for the AES algorithm. IEEE Trans. Circuits Syst. II Express Briefs 53(10), 1153–1157 (2006)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant 61376025, the Industry-academic Joint Technological Innovations Fund Project of Jiangsu under Grant BY2013003-11.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ning Wu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Wu, N., Zhang, X., Ye, Y., Lan, L. (2014). A New Common Subexpression Elimination Algorithm for Constant Matrix Multiplications Over Binary Field. In: Kim, H., Ao, SI., Amouzegar, M. (eds) Transactions on Engineering Technologies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9115-1_11

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-9115-1_11

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-9114-4

  • Online ISBN: 978-94-017-9115-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics