SIAM Journal on Computing
Processor-efficient exponentiation in finite fields
Information Processing Letters
Comparison of three modular reduction functions
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
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
Efficient parallel exponentiation in GF(2n) using normal basis representations
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Handbook of Applied Cryptography
Handbook of Applied Cryptography
MPI-The Complete Reference, Volume 1: The MPI Core
MPI-The Complete Reference, Volume 1: The MPI Core
A Survey of Hardware Implementation of RSA (Abstract)
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th 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
Parallel algorithms for algebraic problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
International Journal of Parallel Programming - Special issue on the 19th international symposium on computer architecture and high performance computing (SBAC-PAD 2007)
Fast exponentiation with precomputation
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Parallel computation of modular exponentiation for fast cryptography
International Journal of High Performance Systems Architecture
New directions in cryptography
IEEE Transactions on Information Theory
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The modular exponentiation operation of the current algorithms for asymmetric cryptography is the most expensive part in terms of computational cost. The RSA algorithm, for example, uses the modular exponentiation algorithm in encryption and decryption procedure. Thus, the overall performance of those asymmetric cryptosystems depends heavily on the performance of the specific algorithm used for modular exponentiation. This work proposes new parallel algorithms to perform this arithmetical operation and determines the optimal number of processors that yields the greatest speedup. The optimal number is obtained by balancing the processing load evenly among the processors. Practical implementations are also performed to evaluate the theoretical proposals.