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We propose a new variant of identity-based encryption named as exclusion-intersection encryption: Intersection decryption keys (e.g., A ? B ? C) generated by a key generation centre can only be used to decrypt the ciphertext which is of all the specified groups| interests, its holders are excluded from decrypting when the documents are not targeted to all these groups (e.g., the key of A ? B ? C cannot decrypt the ciphertext targeted only to C). While recent advances in cryptographic techniques can support a more general access control policy, the private key size is often not a constant. We also present an online/offline variant.