Anamorphic commitment: robust privacy under coercion and parameter tampering

A commitment protocol enables a sender to fix a message without revealing or altering it until later, which is crucial for various cryptographic protocols and applications. However, traditional commitments risk coercion, where an entity, named dictator, can force premature opening or involuntary commitments. This coercive entity was initially explored in encryption by Persiano et al. at EUROCRYPT'22. This work investigates how to circumvent the dictator in commitment, considering the dictator's enhanced ability to influence the sender by tampering with public parameters. We note that from inception to today, commitments were defined and employed under a passive adversary, and this work, therefore, conceptually demonstrates how the “anamorphic perspective” can enrich the relevant adversarial settings of basic primitives. Specifically, we formalize dictator's capabilities for undermining commitments—ranging from weak to strong models—and establish reductions among them. To counter coercion, we propose “anamorphic commitment", a novel primitive that allows the sender to embed a covert message within an innocent-looking commitment to alert to coercion or transmit secret information. We define the syntax, security models, and robustness of anamorphic commitment, and present two generic constructions with distinct performance advantages that can integrate seamlessly with the standard commitments.