The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
VHDL: Analysis and Modeling of Digital Systems
VHDL: Analysis and Modeling of Digital Systems
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Four Hardware Implementations for the M-ary Modular Exponentiation
ITNG '06 Proceedings of the Third International Conference on Information Technology: New Generations
Co-design for System Acceleration: A Quantitative Approach
Co-design for System Acceleration: A Quantitative Approach
Fast hardware for modular exponentiation with efficient exponent pre-processing
Journal of Systems Architecture: the EUROMICRO Journal
Integration, the VLSI Journal - Special issue: Embedded cryptographic hardware
Efficient Hardware for Modular Exponentiation Using the Sliding-Window Method
ITNG '07 Proceedings of the International Conference on Information Technology
Parallel computation of modular exponentiation for fast cryptography
International Journal of High Performance Systems Architecture
Efficient hardware for modular exponentiation using the sliding-window method
International Journal of High Performance Systems Architecture
Parallel modular exponentiation using load balancing without precomputation
Journal of Computer and System Sciences
A massively parallel hardware for modular exponentiations using the m-ary method
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part II
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Modular exponentiation is a basic operation in various applications, such as cryptography. Generally, the performance of this operation has a tremendous impact on the efficiency of the whole application. Therefore, many researchers have devoted special interest to providing smart methods and efficient implementations for modular exponentiation. One of these methods is the sliding-window method, which preprocesses the exponent into zero and non-zero partitions. Zero partitions allow for a reduction of the number of modular multiplications required in the exponentiation using the sliding-window method. The partitioning strategy used allows variable-length non-zero partitions, which increases the average number of zero partitions and so decreases that of non-zero partitions. It performs the partitioning process in parallel with the pre-computation step of the exponent so no overhead is introduced. The implementation is efficient when compared against related existing hardware implementations.