Publication 2002 Issue No. 5 - May Abstract - Montgomery Multiplier and Squarer for a Class of Finite Fields
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Montgomery Multiplier and Squarer for a Class of Finite Fields
May 2002 (vol. 51 no. 5)
pp. 521-529
 ASCII Text x H. Wu, "Montgomery Multiplier and Squarer for a Class of Finite Fields," IEEE Transactions on Computers, vol. 51, no. 5, pp. 521-529, May, 2002.
 BibTex x @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 = {0018-9340},year = {2002},pages = {521-529},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 - JOURJO - IEEE Transactions on ComputersTI - Montgomery Multiplier and Squarer for a Class of Finite FieldsIS - 5SN - 0018-9340SP521EP529EPD - 521-529A1 - H. Wu, PY - 2002KW - Finite fields arithmeticKW - hardware architectureKW - Montgomery multiplicationKW - elliptic curve cryptographyVL - 51JA - IEEE Transactions on ComputersER -

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 bit-parallel 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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Index Terms:
Finite fields arithmetic, hardware architecture, Montgomery multiplication, elliptic curve cryptography
Citation:
H. Wu, "Montgomery Multiplier and Squarer for a Class of Finite Fields," IEEE Transactions on Computers, vol. 51, no. 5, pp. 521-529, May 2002, doi:10.1109/TC.2002.1004591
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