We initiate a systematic treatment of the communication complexity of conditional disclosure of
secrets (CDS), where two parties want to disclose a secret to a third party if and only if their respective inputs
satisfy some predicate. We present a general upper bound and the first non-trivial lower bounds for conditional
disclosure of secrets. Moreover, we achieve tight lower bounds for many interesting setting of parameters for
CDS with linear reconstruction, the latter being a requirement in the application to attribute-based encryption.
In particular, our lower bounds explain the trade-off between ciphertext and secret key sizes of several existing
attribute-based encryption schemes based on the dual system methodology.