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» Fast Integer Multiplication using Modular Arithmetic
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SPAA
1990
ACM
13 years 11 months ago
Hardware Speedups in Long Integer Multiplication
We present various experiments in Hardware/Software designtradeoffs met in speeding up long integer multiplications. This work spans over a year, with more than 12 different hardw...
Mark Shand, Patrice Bertin, Jean Vuillemin
IPL
1998
177views more  IPL 1998»
13 years 7 months ago
A Common-Multiplicand Method to the Montgomery Algorithm for Speeding up Exponentiation
A common-multiplicand method to the Montgomery algorithm makes an improvement in speed when the right-to-left binary exponentiation is applied. The idea is that the same common pa...
JaeCheol Ha, Sang-Jae Moon
FOCS
2000
IEEE
13 years 11 months ago
Computing the Determinant and Smith Form of an Integer Matrix
A probabilistic algorithm is presented to find the determinant of a nonsingular, integer matrix. For a matrix A ¡£¢ n¤ n the algorithm requires O¥ n3¦5 ¥ logn§ 4¦5§ bit...
Wayne Eberly, Mark Giesbrecht, Gilles Villard
CORR
2007
Springer
114views Education» more  CORR 2007»
13 years 7 months ago
Fast Recursive Coding Based on Grouping of Symbols
— A novel fast recursive coding technique is proposed. It operates with only integer values not longer 8 bits and is multiplication free. Recursion the algorithm is based on indi...
Nikolay N. Ponomarenko, Vladimir V. Lukin, Karen O...
AINA
2003
IEEE
14 years 20 days ago
Fast Algorithms for Common-Multiplicand Multiplication and Exponentiation by Performing Complements
The multiplications of common multiplicands and exponentiations of large integers with a large modulus are the primary computation operations in several well-known public key cryp...
Chin-Chen Chang, Ying-Tse Kuo, Chu-Hsing Lin