Overlap-free Karatsuba-Ofman Polynomial Multiplication Algorithm

Published in 1962 [1], Karatsuba-Ofman algorithm (KOA) was the first integer multiplication method broke the quadratic complexity barrier in positiona l number systems. Due to its simplicity, its polynomial version is widely adopted to design VLSI GF (2) parallel multipliers inGF (2)based cryptosystems [9]-[27]. Two parameters are often use d to measure the performance of a GF (2) parallel multiplier, namely, the space and time complexiti s. The space complexity is often represented in terms of the total number of 2-input X OR and AND gates used. The corresponding time complexity is given in terms of the maxim um delay faced by a signal due to these XOR and AND gates. Symbols “ TA” and “TX” are often used to represent the delay of one 2-input AND and XOR gates, respectively.

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