Elliptic curves in cryptography
Elliptic curves in cryptography
Efficient elliptic curve exponentiation
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
ISC '02 Proceedings of the 5th International Conference on Information Security
A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Fast Implementation of Public-Key Cryptography ona DSP TMS320C6201
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and Cryptography
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
On the evaluation of powers and related problems
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
Fast elliptic curve arithmetic and improved weil pairing evaluation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Mycrypt'05 Proceedings of the 1st international conference on Progress in Cryptology in Malaysia
Efficient scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
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In the execution on a smart card, elliptic curve cryptosystems have to be secure against side channel attacks such as the simple power analysis (SPA), the differential power analysis (DPA), and the refined power analysis (RPA), and so on. MMM-algorithm proposed by Mamiya, Miyaji, and Morimoto is a scalar multiplication algorithm secure against SPA, DPA, and RPA, which can decrease the computational complexity by increasing the size of a pre-computed table. However, it provides only 4 different cases of pre-computed tables. From the practical point of view, a wider range of time-memory tradeoffs is usually desired. This paper generalizes MMM-algorithm to improve the flexibility of tables as well as the computational complexity. Our improved algorithm is secure, efficient and flexible for the storage size.