Localized electromagnetic analysis of cryptographic implementations

High resolution inductive probes enable precise measurements of the electromagnetic field of small regions on integrated circuits. These precise measurements allow to distinguish the activity of registers on the circuit that are located at different distances to the probe. This location-dependent information can be exploited in side-channel analyses of cryptographic implementations. In particular, cryptographic algorithms where the usage of registers depends on secret information are affected by side-channel attacks using localized electromagnetic analysis. Binary exponentiation algorithms which are used in public key cryptography are typical examples for such algorithms. This article introduces the concept of localized electromagnetic analysis in general. Furthermore, we present a case study where we employ a template attack on an FPGA implementation of the elliptic curve scalar multiplication to prove that location-dependent leakage can be successfully exploited. Conv entional countermeasures against side-channel attacks are ineffective against location-dependent side-channel leakage. As an effective general countermeasure, we promote that the assignment of registers to physical locations should be repeatedly randomized during execution.