Publication 2002 Issue No. 11 - November Abstract - Finite Field Multiplier Using Redundant Representation
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Finite Field Multiplier Using Redundant Representation
November 2002 (vol. 51 no. 11)
pp. 1306-1316
 ASCII Text x Huapeng Wu, M. Anwar Hasan, Ian F. Blake, Shuhong Gao, "Finite Field Multiplier Using Redundant Representation," IEEE Transactions on Computers, vol. 51, no. 11, pp. 1306-1316, November, 2002.
 BibTex x @article{ 10.1109/TC.2002.1047755,author = {Huapeng Wu and M. Anwar Hasan and Ian F. Blake and Shuhong Gao},title = {Finite Field Multiplier Using Redundant Representation},journal ={IEEE Transactions on Computers},volume = {51},number = {11},issn = {0018-9340},year = {2002},pages = {1306-1316},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2002.1047755},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Finite Field Multiplier Using Redundant RepresentationIS - 11SN - 0018-9340SP1306EP1316EPD - 1306-1316A1 - Huapeng Wu, A1 - M. Anwar Hasan, A1 - Ian F. Blake, A1 - Shuhong Gao, PY - 2002KW - Finite field arithmeticKW - cyclotomic ringKW - redundant setKW - normal basisKW - multiplierKW - squaring.VL - 51JA - IEEE Transactions on ComputersER -

Abstract—This article presents simple and highly regular architectures for finite field multipliers using a redundant representation. The basic idea is to embed a finite field into a cyclotomic ring which has a basis with the elegant multiplicative structure of a cyclic group. One important feature of our architectures is that they provide area-time trade-offs which enable us to implement the multipliers in a partial-parallel/hybrid fashion. This hybrid architecture has great significance in its VLSI implementation in very large fields. The squaring operation using the redundant representation is simply a permutation of the coordinates. It is shown that, when there is an optimal normal basis, the proposed bit-serial and hybrid multiplier architectures have very low space complexity. Constant multiplication is also considered and is shown to have an advantage in using the redundant representation.

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Index Terms:
Finite field arithmetic, cyclotomic ring, redundant set, normal basis, multiplier, squaring.
Citation:
Huapeng Wu, M. Anwar Hasan, Ian F. Blake, Shuhong Gao, "Finite Field Multiplier Using Redundant Representation," IEEE Transactions on Computers, vol. 51, no. 11, pp. 1306-1316, Nov. 2002, doi:10.1109/TC.2002.1047755