An Optimization of Tree Topology Based Parallel Cryptography

Table 1

Number of multiplications in binary, CRT, montgomery, and optimized TRSA.

Method	Best case		Average case		Worst case
Binary	General form	𝑘=1024𝑙=60	General form	𝑘=1024𝑙=10	General form	𝑘=1024𝑙=60
	𝑘−1	1023	1.5(𝑘−1)	1535	2(𝑘−1)	2046
TRSA	𝑘−1	1023	1.5(𝑘−1)−0.5𝑙	1505	2(𝑘−1)−𝑙	1986
CRT			3𝑘^2/4+𝑘	787456
Montgomery			2𝑘^2+𝑘	2098176