Ant Colony Optimisation for Fast Modular Exponentiation using the Sliding Window Method

2006 ◽  
pp. 133-147 ◽  
Author(s):  
Nadia Nedjah ◽  
Luiza de Macedo Mourelle
Keyword(s):  
Sliding Window ◽  
Ant Colony ◽  
Modular Exponentiation ◽  
Ant Colony Optimisation ◽  
Window Method ◽  
Sliding Window Method

scholarly journals Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication

2017 ◽  
Vol 4 (1) ◽  
pp. 1304499 ◽  
Author(s):  
Adamu Muhammad Noma ◽  
Abdullah Muhammed ◽  
Zuriati Ahmad Zukarnain ◽  
Muhammad Afendee Mohamed ◽  
Duc Pham
Keyword(s):  
Sliding Window ◽  
Scalar Multiplication ◽  
Modular Exponentiation ◽  
Window Method ◽  
Sliding Window Method

Efficient hardware for modular exponentiation using the sliding-window method

2008 ◽  
Vol 1 (3) ◽  
pp. 199 ◽  
Author(s):  
Rodrigo Martins da Silva ◽  
Nadia Nedjah ◽  
Luiza de Macedo Mourelle
Keyword(s):  
Sliding Window ◽  
Modular Exponentiation ◽  
Window Method ◽  
Sliding Window Method

A HARDWARE/SOFTWARE CO-DESIGN VERSUS HARDWARE-ONLY IMPLEMENTATION OF MODULAR EXPONENTIATION USING THE SLIDING-WINDOW METHOD

2009 ◽  
Vol 18 (02) ◽  
pp. 295-310 ◽  
Author(s):  
NADIA NEDJAH ◽  
LUIZA DE MACEDO MOURELLE
Keyword(s):  
Embedded System ◽  
Sliding Window ◽  
Modular Exponentiation ◽  
Basic Operation ◽  
Constant Length ◽  
Window Method ◽  
Sliding Window Method ◽  
On Chip ◽  
Tremendous Impact ◽  
Partitioning Strategy

Modular exponentiation is a basic operation in cryptosystems. Generally, the performance of this operation has a tremendous impact on the efficiency of the whole application. The efficiency of the modular exponentiation, in turn, depends mainly on that of modular multiplications as the former is somehow a repetition of the latter. One of the methods that computes the modular power is the sliding-window method, which pre-processes the exponent into zero and nonzero partitions. Zero partitions allow for a reduction of the number of modular multiplications required in the exponentiation process. In this paper, we devise a novel System-on-Chip (SoC) implementation for computing modular exponentiation using the sliding-window method. We also propose a hardware-only implementation for that operation. The partitioning strategy used in both approaches allows constant-length nonzero partitions, which increases the average number of zero partitions and so decreases that of nonzero partitions. The partitioning strategy allows variable-length zero partitions. The hardware/software co-design implements the modular multiplication on hardware and the rest of the system in software. We provide a useful comparison of the SoC-based implementation against hardware-only implementation. Both of the proposed implementations can be used in any industrial embedded system that needs to secure the handled information.

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