High Performance M-Term Karatsuba-Like Multiplier for Finite Field Arithmetic

Abstract

Abstract: Finite field multiplication plays a crucial role in cryptographic circuits due to its widespread application. However, building circuits for these multiplications poses significant challenges due to their complexity. To mitigate this, the Karatsuba algorithm is employed, dividing each number into n/2 bits to reduce space complexity. While this approach reduces space complexity, it also increases time complexity. In our research, we introduce a hybrid approach, implementing a Karatsuba-like multiplier that combines elements of both Karatsuba and SBM (school book multiplication) techniques. Here in the proposed design, we replace the Array multiplier with a Wallace tree multiplier to further enhance design performance. This combination effectively reduces both time and space complexity. Our findings, based on reported device utilization and latency, demonstrate that the proposed multiplier outperforms the standard Karatsuba multiplier in terms of speed and efficiency, particularly in the area–delay product metric.