The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Toward Correctly Rounded Transcendentals
IEEE Transactions on Computers
Journal of Automated Reasoning
Small Multiplier-Based Multiplication and Division Operators for Virtex-II Devices
FPL '02 Proceedings of the Reconfigurable Computing Is Going Mainstream, 12th International Conference on Field-Programmable Logic and Applications
Five, Six, and Seven-Term Karatsuba-Like Formulae
IEEE Transactions on Computers
Low-Weight Polynomial Form Integers for Efficient Modular Multiplication
IEEE Transactions on Computers
Integer and polynomial multiplication: towards optimal toom-cook matrices
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
A low-complexity LUT-based squaring algorithm
Computers & Mathematics with Applications
Efficient 15,360-bit RSA using woop-optimised montgomery arithmetic
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Iterative Toom-Cook methods for very unbalanced long integer multiplication
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
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Methods of squaring and multiplying large integers are discussed. The obvious O(n/sup 2/) methods turn out to be best for small numbers. Existing O(n/sup log/ /sup 3/log/ /sup 2/)/spl ap/O(n/sup 1.585/) methods become better as the numbers get bigger. New methods that are O(/sup log5/log/ /sup 3/)/spl ap/0(n/sup 1.465/), O(n/sup log/ /sup 7/log/ /sup 4/)/spl ap/O(n/sup 1.404/), and O(n/sup log/ /sup 9/log/ /sup 5/)/spl ap/O(n/sup 1.365/) presented. In actual experiments, all of these methods turn out to be faster than FFT multipliers for numbers that can be quite large (