• RAZIA SULTANA

Finite field or Galois field arithmetic is becoming increasingly a very important solution for calculations in many applications like wireless or mobile communication systems, satellite communication systems, storage systems, crypto systems, etc. This paper presents a modified multiplier based on Karatsuba multiplication algorithm. To optimize the Karatsuba multiplication algorithm, the product terms are splited into two alternative forms and all the terms are expressed in the repeated fashion. We generalize the modified algorithm for any input bit GF field application. We have compared our proposed multiplier with karatsuba multiplier with respect to complexity. We have also given the general equation for hardware requirement for any field. Less no. of additions is required by our proposed multiplier. The overall area of modified multiplier is improved by 53.75% (over without reduction) & 52.08% (over with reduction). Proposed multiplier is also faster than actual karatsuba multiplier by 3.63% (over without reduction) & 3.91% (over with reduction). The proposed architecture has been simulated and synthesized by Xilinx ISE 14.7 design suite for Vertex , Spartan and Artix 7 device family. The new architecture is simple & easy. Common Expression Elimination (CSE) is applied in the proposed Modified Karatsuba Multiplier (MKM).It is also faster than M-Term Karatsuba algorithm .and it is also applied to compute the circular convolution for DSP application. In Vertex5 FPGA device family, computation of 8-bit circular convolution using Modified Karatsuba Algorithm (MKA) is 23.69% faster than Karatsuba Algorithm (KA). It also consumes 68.69% less slices than existing KA based Convolution.

Karatsuba Algorithm; Finite fields; FPGA; VLSI; polynomial multiplication; Circular Convolution.Common Expression Elimination (CSE).

"AN IMPROVED GENERALIZED KARATSUBA MULTIPLIER IN GF(2m) FIELD AND IT’S CONVOLUTION APPLICATION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.9, Issue 9, page no.b604-b611, September-2022, Available :http://www.jetir.org/papers/JETIR2209173.pdf

"AN IMPROVED GENERALIZED KARATSUBA MULTIPLIER IN GF(2m) FIELD AND IT’S CONVOLUTION APPLICATION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.9, Issue 9, page no. ppb604-b611, September-2022, Available at : http://www.jetir.org/papers/JETIR2209173.pdf