Balanced point operations for side-channel protection of elliptic curve cryptography
Lejla Batina, Nele Mentens, Bart Preneel, Ingrid M.R. Verbauwhede · IEE proceedings. Information security · 2005
The authors propose balanced algorithms for elliptic curve cryptography (ECC). The authors make the point addition and doubling balanced; that is, they are implemented as identical sequences of operations. As an example the authors implement an ECC point multiplication algorithm, using the approach of Montgomery, for which a single power trace does not expose the Hamming weight nor the bits of the secret key. Nevertheless, their field-programmable gate array implementation is also compact and efficient. The proposed multiplier for the finite field operations is digit serial and scalable to arbitrary bit-lengths. The method calculates the result by splitting the multiplication into two separate processes. The architecture presented compares favourably with designs presented in the literature. Furthermore, the power consumption graphs show the new implementation has an improved side-channel resistance.