A Design Methodology for Stealthy Parametric Trojans and Its Application to Bug Attacks

Over the last decade, hardware Trojans have gained increasing attention in academia, industry and by government agencies. In order to design reliable countermeasures, it is crucial to understand how hardware Trojans can be built in practice. This is an area that has received relatively scant treatment in the literature. In this contribution, we examine how particularly stealthy Trojans can be introduced to a given target circuit. The Trojans are triggered by violating the delays of very rare combinational logic paths. These are parametric Trojans, i.e., they do not require any additional logic and are purely based on subtle manipulations on the sub-transistor level to modify the parameters of the transistors. The Trojan insertion is based on a two-phase approach. In the first phase, a SAT-based algorithm identifies rarely sensitized paths in a combinational circuit. In the second phase, a genetic algorithm smartly distributes delays for each gate to minimize the number of faults caused by random vectors. As a case study, we apply our method to a 32-bit multiplier circuit resulting in a stealthy Trojan multiplier. This Trojan multiplier only computes faulty outputs if specific combinations of input pairs are applied to the circuit. The multiplier can be used to realize bug attacks, introduced by Biham et al. In addition to the bug attacks proposed previously, we extend this concept for the specific fault model of the path delay Trojan multiplier and show how it can be used to attack ECDH key agreement protocols. Our method is a general approach to path delay faults. It is a versatile tool for designing stealthy Trojans for a given circuit and is not restricted to multipliers and the bug attack.