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In Broadcast Encryption schemes, a sender can broadcast the encrypted message securely in a threatening network to a set of legitimate system users only. In IBE scheme any sender can encrypt the desired message using his/her identity without attaining the public key certificate. Here, we have presented an efficient ID-based broadcast encryption scheme (IBBE) for open networks. In this scheme, desired messages can be broadcasted to any subset of the users by any sender but only authorized receivers are capable in retrieving the encrypted messages. This scheme has shorter decryption keys in comparison with other primitive of IBBE scheme for open networks. Moreover, the proposed scheme intends to achieve the lower cost for computation as well as transmission in comparison to earlier existing IBBE schemes.

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