A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
Finite field for scientists and engineers
Finite field for scientists and engineers
A survey of fast exponentiation methods
Journal of Algorithms
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
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
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Randomized Signed-Scalar Multiplication of ECC to Resist Power Attacks
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Low-Cost Solutions for Preventing Simple Side-Channel Analysis: Side-Channel Atomicity
IEEE Transactions on Computers
Pipelined Computation of Scalar Multiplication in Elliptic Curve Cryptosystems (Extended Version)
IEEE Transactions on Computers
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This paper presents an efficient scheme for computing elliptic curve scalar multiplication that uses side-channel atomicity to resist against SPA attacks. The inherent parallelism within point operations is exploited to perform parallel computations of atomic blocks within the same point operation. The computations of atomic blocks of subsequent point operations are then overlapped to increase the performance. Randomising the scalar multiplier and the projective coordinates are applied together to immunise the scheme against DPA attacks. The results show that the proposed scheme is highly efficient in comparison with the pipelined scheme of Mishra (2006), which outperformed previous schemes.