Evaluating a Side-Channel Resistance against Order 4 Rational Points in Arduino Cryptography Library
Keiji Yoshimoto, Yoshinori Uetake, Yuta Kodera, Takuya Kusaka, Yasuyuki Nogami · 2019
Curve25519 has been used in various security protocols for its efficiency and rapidity. However, Curve25519 is known to have rational points whose orders are 2, 4, and 8. In this research, the authors focus on rational points of order 4 and demonstrate a side-channel attack (SCA) against a scalar multiplication algorithm for Curve25519. It purposes to compare two scalar multiplication algorithms in terms of the difficulty of estimating a secret key via the SCA, where the algorithms are differentiated whether it uses a conditional swap function or not. Furthermore, we examine to attack an open-source library for Arduino UNO which includes the scalar multiplication algorithm using a conditional swap function in practice. Since this library takes a countermeasure against the SCA during key exchange, we can use this secure library as a protocol tool. However, there is a threat when we implement a scalar multiplication by using some functions in this library without considering the SCA.