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H. Wu, "Montgomery Multiplier and Squarer for a Class of Finite Fields," IEEE Transactions on Computers, vol. 51, no. 5, pp. 521529, May, 2002.  
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@article{ 10.1109/TC.2002.1004591, author = {H. Wu}, title = {Montgomery Multiplier and Squarer for a Class of Finite Fields}, journal ={IEEE Transactions on Computers}, volume = {51}, number = {5}, issn = {00189340}, year = {2002}, pages = {521529}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2002.1004591}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Montgomery Multiplier and Squarer for a Class of Finite Fields IS  5 SN  00189340 SP521 EP529 EPD  521529 A1  H. Wu, PY  2002 KW  Finite fields arithmetic KW  hardware architecture KW  Montgomery multiplication KW  elliptic curve cryptography VL  51 JA  IEEE Transactions on Computers ER   
Montgomery multiplication in {\rm GF}(2^m) is defined by a(x)b(x)r^{1}(x)\bmod{f(x)}, where the field is generated by a root of the irreducible polynomial f(x), a(x) and b(x) are two field elements in {\rm GF}(2^m), and r(x) is a fixed field element in {\rm GF}(2^m). In this paper, first, a slightly generalized Montgomery multiplication algorithm in {\rm GF}(2^m) is presented. Then, by choosing r(x) according to f(x), we show that efficient architectures of bitparallel Montgomery multiplier and squarer can be obtained for the fields generated with an irreducible trinomial. Complexities of the Montgomery multiplier and squarer in terms of gate counts and time delay of the circuits are investigated and found to be as good as or better than that of previous proposals for the same class of fields.
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