Side-Channel Analysis of Weierstrass and Koblitz Curve ECDSA on Android Smartphones

In this paper, we study the side-channel resistance of the implementation of the ECDSA signature scheme in Android’s standard cryptographic library. We show that, for elliptic curves over prime fields, one can recover the secret key very efficiently on smartphones using electromagnetic side-channel and well-known lattice reduction techniques. We experimentally show that elliptic curve operations (doublings and additions) can be distinguished in a multi-core CPU clocking over the giga-hertz. We then extend the standard lattice attack on ECDSA over prime fields to binary Koblitz curves. This is the first time that such an attack is described on Koblitz curves. These curves, which are also available in Bouncy Castle, allow very efficient implementations using the Frobenius operation. This leads to signal processing challenges since the number of available points are reduced. We investigate practical side-channel, showing the concrete vulnerability of such implementations. In comparis...

• Type: Journal
• Year: 2016
• Where: CTRSA
• Authors: Pierre Belgarric, Pierre-Alain Fouque, Gilles Macario-Rat, Mehdi Tibouchi
• Keywords: Cryptology, CTRSA 2016