We use multilinear maps to provide a solution to the longstanding problem of public-key broadcast encryption where all parameters in the system are small. In our constructions, ciphertext overhead, private key size, and public key size are all poly-logarithmic in the total number of users. The systems are fully collusion-resistant against any number of colluders. All our systems are based on an O(log N)-way multilinear map to support a broadcast system for N users. We present three constructions based on different types of multilinear maps and providing different security guarantees. Our systems naturally give identity-based broadcast systems with short parameters.
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