The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A survey of fast exponentiation methods
Journal of Algorithms
MIST: An Efficient, Randomized Exponentiation Algorithm for Resisting Power Analysis
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
Sliding Windows Succumbs to Big Mac Attack
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Exponentiation using Division Chains
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
Theory and applications for a double-base number system
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
Delaying and merging operations in scalar multiplication: applications to curve-based cryptosystems
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Efficient and secure elliptic curve point multiplication using double-base chains
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
ISC'07 Proceedings of the 10th international conference on Information Security
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Most exponentiation algorithms are categorised as being left-to-right or right-to-left because of the order in which they use the digits of the exponent. There is clear value in having a canonical way of transforming an algorithm in one direction into an algorithm in the opposite direction: it may lead to new algorithms, different implementations of existing algorithms, improved side-channel resistance, greater insights. There is already an historic duality between left-to-right and right-to-left exponentiation algorithms which shows they take essentially the same time, but it does not treat the space issues that are always so critical in resource constrained embedded crypto-systems. To address this, here is presented a canonical duality which preserves both time and space. As an example, this is applied to derive a new, fast yet compact, left-to-right algorithm which makes optimal use of recently developed composite elliptic curve operations.