Efficient Big Integer Multiplication and Squaring Algorithms for Cryptographic Applications

Table 1

Comparison of the well-known polynomial multiplication algorithms.

Multiplication algorithm	Technique			Representation	Complexity
	Divide and conquer	Point evaluation	Interpolation
Classical	—	—	—	Coefficient representation	𝑂𝑛^2
Karatsuba	√	—	—	Coefficient representation	𝑂𝑛^1.58
Toom-Cook	√	√	√	Point-value representation	𝑂𝑛^log(2𝑘−1)/log𝑘
FFT	√	√	√	Point-value representation	𝑂𝑛log𝑛loglog𝑛