Fast multiplication techniques for public key cryptography

We describe two novel techniques for multiplying polynomials which help with accelerating popular public key cryptographic algorithms like RSA and key exchange techniques like Elliptic Curve Diffie Hellman. The first technique is based on an algorithm for generating one-iteration Karatsuba-like formulae using graphs. The novelty of our approach lies on the correlation between graph properties (i.e. vertices, edges and sub-graphs) and the Karatsuba-like terms of big number multiplication routines. The second technique is an improvement over the one-iteration extension to Karatsuba proposed by Weimerskirch and Paar (2003) that yields better performance when the input polynomials have odd number of coefficients. We present experimental data that show that our techniques boost the performance of public key and key exchange algorithms substantially.