Real Symmetric Bilinear Functions and Fast Multiplication of Multi-precision Integers
Xiao Wang · 2007
The efficiency of multiplication of multi-precision integers determines that of modular multiplication and modular exponential algorithms in public key cryptographic systems. Toom-Cook algorithm is a kind of widely used fast multiplication algorithm for multi-precision integers, and current primary research method of this algorithm is the theory of interpolation. With real symmetric bilinear functions and quadratic form, the algebraic representation form of all Toom-Cook parameters and how to search a fast algorithm are provided in this paper, some practical multiplication and squaring algorithms are prior to or same as current best results. The research results show that it’s more advantageous to analyzing the efficiency of algorithms and get the optimal algorithms with real symmetric bilinear functions and quadratic form than with interpolation.