Elliptical Curve Scalar Multiplication over Pipelined Architecture - GF(2m)

An attempt to propose a novel scheme for multiplications through finite field inclusive of Elliptic Curve computations. A serial finite field multiplier i.e.., consider the word length w, for the scalar multiplication is subjected to Implementation, performing a scalar computation in clock cycles with corresponding gate delays within the critical path. The designing and operation characteristics of this mechanism is explained thoroughly. Elliptic curve scalar multiplication operations commonly correspond to finite field (FF) executions i.e., addition, multiplication, subtraction, and inversion. By breaking down the addition and doubling operations into FF operations we obtain the parallel and pipelined scalar multiplication resulting in finite field subtraction, squaring, addition, inversion, and multiplication operations, respectively. The proposed scheme refers to one such mechanism of elliptical curve scalar multiplications over finite field.