Hardware Implementation of Montgomery's Modular Multiplication Algorithm
IEEE Transactions on Computers
Practical genetic algorithms
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
High-Radix Montgomery Modular Exponentiation on Reconfigurable Hardware
IEEE Transactions on Computers
Multi-Agent Systems: An Introduction to Distributed Artificial Intelligence
Multi-Agent Systems: An Introduction to Distributed Artificial Intelligence
Systolic Modular Multiplication
IEEE Transactions on Computers
Modular Exponentiation on Fine-Grained FPGA
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
A Survey of Hardware Implementation of RSA (Abstract)
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Efficient Parallel Modular Exponentiation Algorithm
ADVIS '02 Proceedings of the Second International Conference on Advances in Information Systems
Montgomery Modular Exponentiation on Reconfigurable Hardware
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
DSD '02 Proceedings of the Euromicro Symposium on Digital Systems Design
A Scalable Architecture for Modular Multiplication Based on Montgomery's Algorithm
IEEE Transactions on Computers
Ant Colony Optimization
Efficient pre-processing for large window-based modular exponentiation using genetic algorithms
IEA/AIE'2003 Proceedings of the 16th international conference on Developments in applied artificial intelligence
Co-design for System Acceleration: A Quantitative Approach
Co-design for System Acceleration: A Quantitative Approach
Integration, the VLSI Journal - Special issue: Embedded cryptographic hardware
A new modular exponentiation architecture for efficient design of RSA cryptosystem
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
International Journal of Parallel Programming - Special issue on the 19th international symposium on computer architecture and high performance computing (SBAC-PAD 2007)
Ant colony system: a cooperative learning approach to the traveling salesman problem
IEEE Transactions on Evolutionary Computation
| Hi-index | 0.00 |
Abstract: Modular exponentiation is an important operation in several public-key cryptosystems. It is performed using successive modular multiplications. For the sake of efficiency, one needs to reduce the total number of required modular multiplications. This paper brings a novel idea based on the principles of ant colony optimization for finding a minimal addition chain that allows for the reduction of the number of modular multiplications required for modular exponentiations. Furthermore, we propose a hardware/software co-design of a system-on-chip implementation to efficiently compute modular exponentiations. The hardware sub-system implements the modular multiplication, which is the basic and time-consuming operation, while the software sub-system implements the search routine for the adequate operands this multiplication within previously computed products. The ant system is always in execution by an available co-processor, trying to improve the addition chain in use by the overall system. The best addition chain reached by the ant system is compared to the one used in the m-ary and sliding window methods as well as to the best addition chain evolved by genetic algorithms. We demonstrate that the ant system significantly outperforms all these methods for any exponent size. We provide a comparison of the proposed implementation with three existing ones using the performance factor, which takes into account both space and time requirements.