CRYPTO '89 Proceedings 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
Concrete Math
Complexity and Fast Algorithms for Multiexponentiations
IEEE Transactions on Computers
On String Replacement Exponentiation
Designs, Codes and Cryptography
Exponentiation Using Division Chains
IEEE Transactions on Computers
Discrete-Log With Compressible Exponents
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Speeding up Elliptic Cryptosystems by Using a Signed Binary Window Method
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Universal Exponentiation Algorithm
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Minimal Weight Digit Set Conversions
IEEE Transactions on Computers
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
New modular multiplication algorithms for fast modular exponentiation
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Resource requirements for the application of addition chains in modulo exponentiation
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
An analysis of exponentiation based on formal languages
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
A loopless gray code for minimal signed-binary representations
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Research note: A fast modular multiplication method based on the Lempel-Ziv binary tree
Computer Communications
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The similarity between fast computations with huge numbers and data compression is investigated. For example, in data-compression, frequent messages are assigned short codes, while in fast computations we store and reuse the results of frequent computations. In compression we sometimes send the difference of consecutive messages, if its usually small (驴 modulation), while in fast computation we compute xn+驴=xn驴x驴, xn is already known, and 驴驴n.We demonstrate the similarity by applying a modification of the Lempel-Ziv data compression algorithm to fast exponentiation, to result runtime which is comparable to the best known methods, in the practical range (500-1000 bits), for random exponents. For compressible exponents we gain on the average the compression ratio. This may be applicable to Diffie-Hellman like cryptographic systems. It is an open question whether compressible exponents are safe.