Paper 2007/393

Overlap-free Karatsuba-Ofman Polynomial Multiplication Algorithms

Haining Fan, Jiaguang Sun, Ming Gu, and Kwok-Yan Lam


We describe how a simple way to split input operands allows for fast VLSI implementations of subquadratic $GF(2)[x]$ Karatsuba-Ofman multipliers. The theoretical XOR gate delay of the resulting multipliers is reduced significantly. For example, it is reduced by about 33\% and 25\% for $n=2^{t}$ and $n=3^{t}$ $(t>1)$, respectively. To the best of our knowledge, this parameter has never been improved since the original Karatsuba-Ofman algorithm was first used to design $GF(2^n)$ multipliers in 1990.

Note: I received an email from Dr. Ekatherina Karatsuba, A. Karatsuba' daughter, and she told me that the Karatsuba algorithm was found by her father himself. So I added the following information on the 1st page. I am sorry that I have made the following mistake: The first subquadratic integer multiplication algorithm was invented by A.A. Karatsuba himself, not Karatsuba and Ofman. [1]

Available format(s)
Publication info
Published elsewhere. IET Information security, vol. 4, no. 1, pp. 8-14, 2010.
Karatsuba algorithmpolynomial multiplicationsubquadratic space complexity multiplierfinite fieldsGalois fields.
Contact author(s)
fhn @ tsinghua edu cn
2010-06-28: last of 6 revisions
2007-10-14: received
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      author = {Haining Fan and Jiaguang Sun and Ming Gu and Kwok-Yan Lam},
      title = {Overlap-free Karatsuba-Ofman Polynomial Multiplication Algorithms},
      howpublished = {Cryptology ePrint Archive, Paper 2007/393},
      year = {2007},
      note = {\url{}},
      url = {}
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