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ARITH
2005
IEEE

Fast Modular Reduction for Large Wordlengths via One Linear and One Cyclic Convolution

10 years 8 months ago
Fast Modular Reduction for Large Wordlengths via One Linear and One Cyclic Convolution
Abstract— Modular reduction is a fundamental operation in cryptographic systems. Most well known modular reduction methods including Barrett’s and Montgomery’s algorithms leverage some-pre computations to avoid divisions so that the main complexity of these methods lies in a sequence of two long multiplications. For large wordlengths a multiplication which is tantamount to a linear convolution is performed via the Fast Fourier Transform (FFT) or other transform-based techniques as in the Schonhage-Strassen multiplication algorithm. We show a fundamental property (the separation principle): in a modular reduction based on long multiplications, the linear convolution required by one of the two long multiplications can be replaced by a cyclic convolution, and the halves can be separated using other information available due to the intrinsic redundancy of the operations. This reduces the number of operations by about 25%. We demonstrate that both Barrett’s and Montgomery’s method...
Dhananjay S. Phatak, Tom Goff
Added 24 Jun 2010
Updated 24 Jun 2010
Type Conference
Year 2005
Where ARITH
Authors Dhananjay S. Phatak, Tom Goff
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