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Security often relies on functions implemented in hardware. But, various types of attacks have been developed, in particular, fault-based attacks allowing a hacker to observe abnormal behaviors from which secret data can be inferred. Analyzing very early, during a circuit design, the potential impact of faults therefore becomes necessary to avoid security flaws. Dependability analysis environments have been developed to analyze the effect of "natural" faults, for example, those induced by particles. This paper discusses the similarities and differences between the two types; of application areas and proposes extensions of the classical fault models to cover security-related constraints. Experimental results on a coprocessor for RSA encryption demonstrate the need for such an extended fault model.