A verification of brickell's fast modular multiplication algorithm

Hardware implementation of Montgomery's modular multiplication algorithm

“…Montgomery [9], and further developed by the first author [5] and Dussé and Kaliski [4]. Much more efficient use of hardware is made here than for the standard algorithm of Brickell [1] studied by the present authors in [16], although subsequent work by the second author [15] provides similar improvements for that also. We establish that the new method has a speed approximately twice as fast as previously existing ones.…”

“…So now the choice of q for the input M * in the next iteration depends only on the lowest two digits of the current M * and of the partial product R. The cost of this simplification is just 2 iterations more than the number of digits in the modulus compared with at least 5 in a straightforward application of Brickell's method (see [16]) or 3 if scaling the modulus is done (see [15]). Hence there is essentially no increase in the number of clock cycles for the new algorithm.…”

Hardware architectures for public key cryptography

“…Brickell [26] improved this concept to finish a modular multiplication in only t + 7 clock cycles. A circuit for Brickell's multiplier is described in the work of Walter and Eldridge [208].…”

Two hardware implementations for the Montgomery modular multiplication: sequential versus parallel

“…The entire design was done using the Xilinx Project Manager (version Build 6.00.09) [14] through the steps of the Xilinx design cycle shown in Fig. 10.…”

“…There are various algorithms that implement modular multiplication such as Barrett's and Booth's methods [12], [13], and Brickell's algorithm [14]. Here, we concentrate on the Montgomery's algorithm as it is considered the most popular and more efficient.…”