Exponentiating faster with addition chains
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Exponentiation using canonical recoding
Theoretical Computer Science
Space/Time Trade-Offs for Higher Radix Modular Multiplication Using Repeated Addition
IEEE Transactions on Computers
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Fast Exponentation in Cryptography
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Theory and applications for a double-base number system
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
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
Montgomery's Multiplication Technique: How to Make It Smaller and Faster
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Universal Exponentiation Algorithm
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Some Security Aspects of the M IST Randomized Exponentiation Algorithm
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Fast modular exponentiation of large numbers with large exponents
Journal of Systems Architecture: the EUROMICRO Journal
Hardware architectures for public key cryptography
Integration, the VLSI Journal
Fast scalar multiplication for ECC over GF(p) using division chains
WISA'10 Proceedings of the 11th international conference on Information security applications
| Hi-index | 14.98 |
Exponentiation may be performed faster than the traditional square and multiply method by iteratively reducing the exponent modulo numbers which, as exponents themselves, require few multiplications. This mainly includes those with few nonzero bits. For a suitable choice of such divisors, the resulting mixed basis representation of the exponent reduces the expected number of nonsquaring multiplications by over half at the cost of a single extra register. Preprocessing effort depends entirely on the exponent and can be kept down to the work saved in a single exponentiation. Moreover, no precomputed look-up tables are required, so the method is especially applicable where space is at a premium. In particular, it outperforms the instance of the m-ary method which uses the same space. However, for 512-bit exponents, it beats every instance of the m-ary method, achieving well under 635 multiplications on average. Both hardware and software implementations of the RSA crypto-system can benefit from this algorithm.