This paper shows that quasi-open bisimilarity is the coarsest bisimilarity congruence for the applied $$\pi $$ π -calculus. Furthermore, we show that this equivalence is suited to security and privacy problems expressed as an equivalence problem in the following senses: (1) being a bisimilarity is a safe choice since it does not miss attacks based on rich strategies; (2) being a congruence it enables a compositional approach to proving certain equivalence problems such as unlinkability; and (3) being the coarsest such bisimilarity congruence it can establish proofs of some privacy properties where finer equivalences fail to do so.

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To address privacy problems with the EMV standard, EMVco proposed a Blinded Diffie-Hellman key establishment protocol. We point out that active attackers were not previously accounted for in the privacy requirements of this proposed protocol, despite the fact that an active attacker can compromise unlinkability. Here, we adopt a strong definition of unlinkability that does account for active attackers and propose an enhancement of the protocol proposed by EMVco where we make use of Verheul certificates. We prove that our protocol does satisfy strong unlinkability, while preserving authentication.

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