We consider *semi-adaptive* security for attribute-based encryption,
where the adversary specifies the challenge attribute vector after
it sees the public parameters but before it makes any secret key
queries. We present two constructions of semi-adaptive
attribute-based encryption under static assumptions with *short*
ciphertexts. Previous constructions with short ciphertexts either
achieve the weaker notion of selective security, or require
parameterized assumptions.
As an application, we obtain improved delegation schemes for Boolean
formula with *semi-adaptive* soundness, where correctness of the
computation is guaranteed even if the client's input is chosen
adaptively depending on its public key. Previous delegation schemes
for formula achieve one of adaptive soundness, constant
communication complexity, or security under static assumptions; we
show how to achieve semi-adaptive soundness and the last two
simultaneously.
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