New Versions of Miller-loop Secured against Side-Channel Attacks

Nadia El Mrabet , Loubna Ghammam (1) , Nicolas Méloni (2) , Emmanuel Fouotsa

1 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne
2 IMATH - Institut de Mathématiques de Toulon - EA 2134

In this paper, we propose two new versions of Miller algorithm in order to secure pairing computations against existing side-channel attacks (SCA). We have chosen to use the co-Z arithmetic on elliptic curves from which we derive two methods for pairing computations: one based on Euclidean addition chains and one based on Zeckendorf representation. We show that our propositions are resistant to existing side-channel attacks against pairing-based cryptography. We consider differential power analysis and fault attacks. The complexities of our solutions are compared with state-of-the-art one. We demonstrate that our new proposed versions are more efficient by 17%.

Mots clés: Miller algorithm Euclidean addition chains Fibonacci number optimal Ate pairing sidechannel attacks; Miller algorithm; Euclidean addition chains; Fibonacci number; optimal Ate pairing; sidechannel attacks

Domaines: Cryptographie et sécurité [cs.CR]; Arithmétique des ordinateurs

Nadia El Mrabet, Loubna Ghammam, Nicolas Méloni, Emmanuel Fouotsa. New Versions of Miller-loop Secured against Side-Channel Attacks. Arithmetic of Finite Fields, 13638, Springer International Publishing, pp.269-287, 2023, Lecture Notes in Computer Science, ⟨10.1007/978-3-031-22944-2_17⟩. ⟨hal-03934165⟩