Super-logarithmic lower bounds for conditional disclosure of secrets

Prove super-logarithmic lower bounds for the conditional disclosure of secrets primitive for explicit Boolean functions when protocols are allowed a small error, thereby resolving the stated open problem in classical cryptography.

Background

The paper explains that entanglement cost in the f-BB84 position-verification scheme is related to entanglement cost in f-routing, which in turn lower-bounds the randomness cost of conditional disclosure of secrets (CDS). Establishing super-logarithmic lower bounds for CDS with explicit functions and small error would therefore have consequences for proving strong entanglement lower bounds in f-BB84. The authors identify this as a longstanding unresolved problem in the classical cryptography literature.

References

Finally, proving super-logarithmic lower bounds on CDS is an outstanding open problem in classical cryptography, when we consider explicit choices of function $f$ and allow the protocol to work only up to small errors .

— Quantum gate lower bounds for loss-tolerant position verification  (2608.16495 - May et al., 17 Aug 2026) in Section 1, subsection “Prior work”