Efficient Combined Algorithm for Multiplication and Squaring for Fast Exponentiation over Finite Fields $$GF(2^{m})$$

Novel bit-serial semi-systolic array structure for simultaneously computing field multiplication and squaring

“…They developed bit-serial and bit-parallel systolic array structures based on the proposed approach. Kim et al [14], presented a bit-parallel systolic array structure based on the unified algorithm reported in [15]. This algorithm is based on the bipartite method discussed in [16].…”

Efficient parallel semi-systolic array structure for multiplication and squaring in GF(2<i>^m</i>)

“…In this section, we briefly discuss the unified modular multiplication and squaring algorithm over GF(2 m ) as the details of this algorithm are previously given in [17,19]. Suppose that FðxÞ be the irreducible polynomial used to generate the finite field over GF(2 m ).…”

“…The authors in [17] proposed a unified algorithm to concurrently perform field multiplication and squaring in GF(2 m ) based on the bipartite method. The proposed algorithm is a regular iterative algorithm and enables the parallel implementation of the two operations.…”

“…In [18], authors developed a unified parallel semi-systolic array structure based on the Montgomery multiplication algorithm in GF(2 m ) to concurrently compute field multiplication and squaring. In [19], authors developed a parallel systolic array structure based on the unified algorithm described in [17]. They proved that it has a lower latency and critical path delay over the related systolic structures.…”

“…In this paper, we develop an efficient parallel semisystolic array structure to concurrently compute multiplication and squaring in GF(2 m ) based on the bipartite multiplication method described in [17]. Comparing to the most recent related work of [6,18,19], the developed array structure has a significant reduction in both area and AT complexities.…”