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Some algorithms are more efficient than others. The complexity of an algorithm is a function describing the efficiency of the algorithm which has two measures: Space Complexity and Time Complexity. In this paper, we present complexity analysis for FPGA based designs which is based on 4-input and 1-output LUT structure followed by the majority of FPGA manufacturers. The same procedure is then applied to Karatsuba-Offman Multiplier (KOM) because of two reasons. Firstly, due to the increased use of FPGAs especially for security applications, it seems logical to compare various architectures for their efficiencies in FPGAs. Secondly, for diverse security applications, it provides a prior estimation to hardware resources and achievable timing. We consider a 4-input and 1-output structure as a basic building block available in majority of FPGAs by different FPGA manufacturers. We then compare our theoretical and experimental results for KOM in FPGAs which are fairly convincible.
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