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Unidirectional Two Dimensional Systolic Array for Multiplication in GF(2m) Using LSB First Algorithm

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3849))

Abstract

The two dimensional systolic array for multiplication in binary field GF(2m) with LSB (Least Significant Bit) first algorithm proposed by Yeh et al. has the unfavorable property of bidirectional data flows compared with that of Wang and Lin which use MSB (Most Significant Bit) first algorithm. In this paper, by using a polynomial basis with LSB first algorithm, we present an improved bit parallel systolic array over GF(2m). Our two dimensional systolic array has unidirectional data flows with 7 latches in each basic cell. Therefore our systolic array has a shorter critical path delay and has the same unidirectional data flows to the multipliers with MSB first scheme.

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References

  1. Wang, C.L., Lin, J.L.: Systolic array implementation of multipliers for finite fields GF(2m). IEEE Trans. Circuits Syst. 38, 796–800 (1991)

    Article  Google Scholar 

  2. Yeh, C.S., Reed, I.S., Troung, T.K.: Systolic multipliers for finite fields GF(2m). IEEE Trans. Computers C-33, 357–360 (1984)

    Article  MATH  Google Scholar 

  3. Fenn, S.T.J., Benaissa, M., Taylor, D.: Dual basis systolic multipliers for GF(2m). IEE Proc. Comput. Digit. Tech. 144, 43–46 (1997)

    Article  Google Scholar 

  4. Wozniak, J.J.: Systolic dual basis serial multiplier. IEE Proc. Comput. Digit. Tech. 145, 237–241 (1998)

    Article  Google Scholar 

  5. Lee, C.Y., Lu, E.H., Lee, J.Y.: Bit parallel systolic multipliers for GF(2m) fields defined by all one and equally spaced polynomials. IEEE Trans. Computers 50, 385–393 (2001)

    Article  MathSciNet  Google Scholar 

  6. Zhou, B.B.: A new bit serial systolic multiplier over GF(2m). IEEE Trans. Computers C-37, 749–751 (1988)

    Article  Google Scholar 

  7. Diab, M., Poli, A.: New bit serial systolic multiplier for GF(2m) using irreducible trinomials. Electronics Letters 27, 1183–1184 (1991)

    Article  Google Scholar 

  8. Jain, S.K., Song, L., Parhi, K.K.: Efficient semisystolic architectures for finite field arithmetic. IEEE Trans. VLSI Syst. 6, 101–113 (1998)

    Article  Google Scholar 

  9. Berlekamp, E.R.: Bit-serial Reed-Solomon encoders. IEEE Trans. Inform. Theory 28, 869–874 (1982)

    Article  MATH  Google Scholar 

  10. Wang, M., Blake, I.F.: Bit serial multiplication in finite fields. SIAM J. Disc. Math. 3, 140–148 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  11. Hasan, M.A., Wang, M.Z., Bhargava, V.K.: A modified Massey-Omura parallel multiplier for a class of finite fields. IEEE Trans. Computers 42, 1278–1280 (1993)

    Article  Google Scholar 

  12. Paar, C., Fleischmann, P., Roelse, P.: Efficient multiplier architectures for Galois fields GF(2m). IEEE Trans. Computers 47, 162–170 (1998)

    Article  MathSciNet  Google Scholar 

  13. Itoh, T., Tsujii, S.: Structure of parallel multipliers for a class of finite fields GF(2m). Information and computation 83, 21–40 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  14. Wang, C.L.: Bit-level systolic array for fast exponentiation in GF(2m). IEEE Trans. Computers 43, 838–841 (1994)

    Article  MATH  Google Scholar 

  15. Wang, C.L., Guo, J.H.: New systolic array for C + AB 2, inversion, and division in GF(2m). IEEE Trans. Computers 49, 1120–1125 (2000)

    Article  Google Scholar 

  16. Kwon, S., Kim, C.H., Hong, C.P.: Compact linear systolic arrays for multipliation using a trinomial basis in GF(2m) for high speed cryptographic processors. In: Gervasi, O., Gavrilova, M.L., Kumar, V., Laganá, A., Lee, H.P., Mun, Y., Taniar, D., Tan, C.J.K. (eds.) ICCSA 2005. LNCS, vol. 3480, pp. 508–518. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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Kwon, S., Kim, C.H., Hong, C.P. (2006). Unidirectional Two Dimensional Systolic Array for Multiplication in GF(2m) Using LSB First Algorithm. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds) Fuzzy Logic and Applications. WILF 2005. Lecture Notes in Computer Science(), vol 3849. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11676935_52

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  • DOI: https://doi.org/10.1007/11676935_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32529-1

  • Online ISBN: 978-3-540-32530-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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