Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Discrete Applied Mathematics
Collusion resistant broadcast encryption with short ciphertexts and private keys
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Improved broadcast encryption scheme with constant-size ciphertext
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Improved broadcast encryption scheme with constant-size ciphertext
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
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The Boneh-Gentry-Waters (BGW) [3] broadcast encryption scheme is optimal regarding the overhead size. This performance relies on the use of a pairing. Hence this protocol can benefit from public key improvements. The main lasting constraint is the computation time at receiver end as it depends on the number of revoked users. In this paper we describe two modifications to improve BGW bandwidth and time complexity. First we rewrite the protocol with an asymmetric pairing over Barreto-Naehrig (BN) curves instead of a symmetric one over supersingular curves. This modification leads to a practical gain of 60% in speed and 84% in bandwidth. The second tweaks allows to reduce the computation time from O(n−r) to min (O(r),O(n−r)) for the worst case (and better for the average case). We give performance measures of our implementation for a 128-bit security level of the modified protocol on a smartphone.