Strategies for FPGA Implementation of Non-Restoring Square Root Algorithm

This paper presents three strategies to implement non restoring square root algorithm based on FPGA. A new basic building block is called controlled subtract-multiplex (CSM) is introduced in first strategy which use gate level abstraction. The main principle of the method is similar with conventional non-restoring algorithm, but it only uses subtract operation and append 01, while add operation and append 11 is not used. Second strategy presents the first strategy in register transfer level (RTL) abstraction. In third strategy, a modification for the implementation of conventional non-restoring algorithm is presented which also use RTL abstraction. The all above strategies is implemented in VHDL programming and adopt fully pipelined architecture. The strategies have conducted to implement successfully in FPGA hardware, and each of the strategies is offer an efficient in hardware resource. In generally, the third strategy is superior.DOI:http://dx.doi.org/10.11591/ijece.v4i4.600

Square root computation over even extension fields

This paper presents a comprehensive study of the computation of square roots over finite extension fields. We propose two novel algorithms for computing square roots over even field extensions of the form \F_{q^{2}}, with $q=p^n,$ $p$ an odd prime and $n\geq 1$. Both algorithms have an associate computational cost roughly equivalent to one exponentiation in \F_{q^{2}}. The first algorithm is devoted to the case when $q\equiv 1 \bmod 4$, whereas the second one handles the case when $q\equiv 3 \bmod 4$. Numerical comparisons show that the two algorithms presented in this paper are competitive and in some cases more efficient than the square root methods previously known