Modular Multiplication Algorithm and Implementation Based on Type-ⅡOptimal Normal Basis over GF(2m)
GAO Zhao
WANG Qingnian
FAN Rong
Abstract：In this paper,a new method of using type Ⅱ normal basis for multiplication is proposed.By an efficient linear transformation,the regular basis of GF(2m)is transformed into m-term polynomials over GF(2m).This polynomial can be multi-plied using any polynomial multiplication algorithm and then converted back to a normal basis using the inverse of the transformation described above.The XOR/AND operations required for this scheme are M(m)+2mlog2(m 2),where M(m)depends on the poly-nomial multiplication algorithm chosen.Compared with other normal basis methods,it has smaller resource consumption.The FPGA comprehensive practice shows that this scheme can significantly reduce the number of LUTs.
Keywords：optimal normal basispermuted normal basisnormal basis multiplication
Publication Date：2023-10-20
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：5( 2263-2266,2273 )