Side-Channel Attacks on Quantum-Resistant Supersingular Isogeny Diffie-Hellman

In this paper, we present three side-channel attacks on the quantum-resistant supersingular isogeny Diffie-Hellman (SIDH) key exchange protocol. These refined power analysis attacks target the representation of a zero value in a physical implementation of SIDH to extract bits of the secret key. To understand the behavior of these zero-attacks on SIDH, we investigate the representation of zero in the context of quadratic extension fields and isogeny arithmetic. We then present three different refined power analysis attacks on SIDH. Our first and second attacks target the Jao, De Feo, and Plut three-point Montgomery ladder by utilizing a partial-zero attack and zero-value attack, respectively. Our third attack proposes a method to break the large-degree isogeny by utilizing zero-values in the context of isogenies. The goal of this paper is to illustrate additional security concerns for an SIDH static-key user.