An Efficient Countermeasure against Side Channel Attacks for Pairing Computation

Abstract

Pairing-based cryptosystems have been widely researched, and several efficient hardware implementations of pairings have also been proposed. However, side channel attacks (SCAs) are serious attacks on hardware implementations. Whelan et al. pointed out that pairings except the η T pairing might not be vulnerable against SCAs by setting the secret point to the first parameter [25]. This paper deals with SCAs for the η T pairing over \({\mathbb F}_{3^n}\). To our knowledge, the randomized-projective-coordinate method has the smallest overhead among all countermeasures against SCAs for the η T pairing. The cost of that overhead is 3nM, where M is the cost of a multiplication in \({\mathbb F}_{3^n}\). In this paper, we propose another countermeasure based on random value additions (x p + λ) and (y p + λ), where P = (x p ,y p ) is the input point, and λ is a random value in \({\mathbb F}_{3^n}\). The countermeasure using the random value addition was relatively slow in the case of the scalar multiplication of elliptic curve cryptosystems. However, in the case of the η T pairing, we can construct an efficient countermeasure due to the form of the function \(g_P(x,y) = y_p^3y -(x_p^3+x-1)^2\) for a point P = (x p ,y p ). The overhead of our proposed scheme is just 0.5nM, which is a reduction of more than 75% compared with the randomized-projective-coordinate method.