Design And Implementation of an M-Term Karatsuba-Like Polynomial Multiplier for Finite Field Arithmetic

Abstract

The abstract of a Karatsuba multiplier employing a combination of 32-term Karatsuba algorithm, Schoolbook multiplication, adders, shifting bits, and recursive Karatsuba operations would highlight the hybrid nature of the approach and its potential advantages in terms of efficiency and speed. The Karatsuba algorithm is renowned for its divide-and-conquer strategy, which efficiently breaks down large multiplication tasks into smaller sub-problems, thereby reducing computational complexity. The utilization of a 32-term Karatsuba variant enhances its ability to handle larger operands effectively. Schoolbook multiplication, a conventional multiplication technique, is incorporated into the algorithm to leverage its simplicity and straightforward implementation, particularly for smaller operand sizes. Adders, fundamental arithmetic units, play a pivotal role in the multiplier, facilitating the addition of partial products and intermediate results efficiently. Shifting bits are utilized to manipulate binary numbers, aiding in the alignment of operands and computation of partial products. The integration of these techniques creates a hybrid multiplier architecture that capitalizes on the strengths of both Karatsuba and Schoolbook multiplication methods, resulting in improved performance and efficiency. This approach holds promise for accelerating multiplication operations in various computational tasks, including digital signal processing, cryptography, and computer arithmetic.