This paper presents two new public key broadcast encryption systems that are fully secure against any number of colluders. The first system has constant size ciphertexts and private keys for any subset of receivers, with public key size linear in the total number of receivers. The second system generalizes the first, offering a tradeoff between ciphertext size and public key size, achieving O(√n) size for both ciphertexts and public keys for any subset of receivers. The systems are designed for arbitrary receiver sets and are efficient for both small and large broadcast sets. The first system is suitable for applications like encrypted file systems where public keys can be stored in shared storage, while the second is better for content protection where both public key and ciphertext size need to be minimized. The systems are proven secure under the bilinear Diffie-Hellman Exponent assumption. The paper also discusses several applications, including encrypted file systems, encrypted email for large mailing lists, and DVD content protection. The systems are extended to be chosen-ciphertext secure using a combination of identity-based encryption and signature schemes. The paper concludes with open problems, including the construction of a broadcast encryption system secure against adaptive adversaries with the same parameters as the proposed systems.This paper presents two new public key broadcast encryption systems that are fully secure against any number of colluders. The first system has constant size ciphertexts and private keys for any subset of receivers, with public key size linear in the total number of receivers. The second system generalizes the first, offering a tradeoff between ciphertext size and public key size, achieving O(√n) size for both ciphertexts and public keys for any subset of receivers. The systems are designed for arbitrary receiver sets and are efficient for both small and large broadcast sets. The first system is suitable for applications like encrypted file systems where public keys can be stored in shared storage, while the second is better for content protection where both public key and ciphertext size need to be minimized. The systems are proven secure under the bilinear Diffie-Hellman Exponent assumption. The paper also discusses several applications, including encrypted file systems, encrypted email for large mailing lists, and DVD content protection. The systems are extended to be chosen-ciphertext secure using a combination of identity-based encryption and signature schemes. The paper concludes with open problems, including the construction of a broadcast encryption system secure against adaptive adversaries with the same parameters as the proposed systems.