  In this work we present a new structure for multiplication in finite fields.
This structure is based on a digit-level LFSR (Linear Feedback Shift Register)
multiplier in which the area of digit-multipliers are reduced using the
Karatsuba method. We compare our results with the other works in the literature
for F_{3^97}. We also propose new formulas for multiplication in F_{3^{6*97}}.
These new formulas reduce the number of F_{3^97}-multiplications from 18 to 15.
The fields F_{3^{97}} and F_{3^{6*97}} are relevant in the context of
pairing-based cryptography.
