Polynomial Basis Multiplier Using Cellular Systolic Architecture

Efficient unified semi-systolic arrays for multiplication and squaring over <i>GF</i>(2<i>^m</i>)

“…Let k ¼ bm=2c and l ¼ dm=2e. For deriving an efficient parallel architecture, we choose the Montgomery factor, F ¼ x bm=2c ¼ x k as selected in [5,7]. Then, we can derive the following formula for the Montgomery multiplication P and squaring S over GFð2 m Þ.…”

“…Thereafter, Kim and Jeon [5,7] adapted their bipartite technique to the modular multiplication in the finite fields for reducing the latency and proposed multipliers over GFð2 m Þ.…”

“…We adopt the bipartite modular multiplication concept [10,11,5,7] to decrease the latency required for calculating multiplication and squaring over finite fields. Using common-multiplicand method [6,13,14], we also decrease the space complexity by deriving common operations from bipartite parts.…”

“…Modular exponentiation and inversion can be performed using a sequence of multiplications. Although many multiplier over GFð2 m Þ have been proposed [3,4,5,6,7], their high space and time complexities are major limitations in various applications. The Montgomery multiplication algorithm has been proposed for fast modular integer multiplication [8].…”

“…They focused on application in the integer and mentioned the usability of their method in the finite field. Thereafter, Kim and Jeon adapted their bipartite technique to the modular multiplication in the finite fields for reducing the latency and proposed multipliers over GFð2 m Þ [5,7].…”