Fast on-line integer multiplication

Fast arithmetic for faster integer multiplication

For almost 35 years, Schönhage-Strassen’s algorithm has been the fastest algorithm known for multiplying integers, with a time complexity O(n · log n · log log n) for multiplying n-bit inputs. In 2007, Fürer proved that there exists K > 1 and an algorithm performing this operation in O(n · log n · Klog∗ ). Recent work showed that this complexity estimate can be made more precise with K = 8, and...

Fast multiplication of integer matrices Withdrawn paper

Erratum. Eric Schost discovered a bug in this paper: by construction, formula (7) does not hold, since the matrix Va,n is not invertible whenever l> 2. Unfortunately, we do not see how to repair this bug: not only Va,n is not invertible, but the rank of Va,n is actually very small (and equal to max {q1, , ql}). This makes the proof collapse. We have also tried a few other things, such as fixing...

Fast Modular Reduction for Large-Integer Multiplication

This online database contains the full-text of PhD dissertations and Masters' theses of University of Windsor students from 1954 forward. These documents are made available for personal study and research purposes only, in accordance with the Canadian Copyright Act and the Creative Commons license—CC BY-NC-ND (Attribution, Non-Commercial, No Derivative Works). Under this license, works must alw...

Integer Decomposition for Fast Scalar Multiplication on Elliptic Curves

Since Miller and Koblitz applied elliptic curves to cryptographic system in 1985[3,6], a lot of researchers have been interested in this field and various speedup techniques for the scalar multiplication have been developed. Recently, Gallant et al. published a method that accelerates the scalar multiplication and is applicable to a larger class of curves[4]. In the process of their method, the...

Large Integer Multiplication on Hypercubes