Simulatability versus Indistinguishability SOA: CCA Relations are Sampler-Dependent

Contrary to expectation, we show that there is no general reduction from simulation-based selective opening security (SSO) to indistinguishability-based selective opening security (ISO) in the CCA setting. In particular, we show that when restricted to certain message distributions, SSO-CCA is incomparable with ISO-CCA. This contrasts the CPA case, where SSO-CPA is known to be strictly stronger than ISO-CPA relative to any message sampler. Any sampler with high enough min-entropy suffices for this “semi-separation” to appear. On the other hand, we show that restricting to distributions with very low min-entropy gives rise to an implication. Our main result does not rely on the presence of selective openings, but rather follow from subtleties in the game structures. At a glance, this may seem to contradict known equivalences between indistinguishability, semantic security, and selective opening security under trivial openings. We reconcile the apparent contradiction by showing that the CCA landscape splits into a “high-entropy” and a “low-entropy” world, which for notions of SOA must be treated separately.