Methods, components and systems for implementing secure and efficient broadcast encryption schemes with configurable and practical tradeoffs among a pre-broadcast transmission bandwidth t, a key storage cost k, and a key derivation cost c, in which the schemes use subtree difference and key decomposition to generate secondary keys, use the secondary keys to encrypt the broadcast and generate ciphertexts, and use the RSA encryption scheme to implement derivability between the primary keys and the secondary keys. To decrypt the broadcast, a privileged user uses one of its primary keys to derive a secondary key, which is used to decrypt the broadcast. The product of key derivation costc and the key storage cost k is at most (2a-log a-2)log.sub.a n, when n is the number of users, 1.ltoreq.b.ltoreq.log n, a=2.sup.b, and revoked users r