Expressive Bandwidth-Efficient Attribute Based Signature and Signcryption in Standard Model

Abstract

This paper proposes an efficient key-policy attribute based signature (ABS) scheme with constant-size signature for expressive linear secret-sharing scheme (LSSS)-realizable monotone access structures with only 3 pairings for the verification algorithm, which is an affirmative answer for one of the open problems left in Pairing 2012 by Gagn\(\rm{\acute{e}}\) et al. Our ABS provides signer privacy, and the existential unforgeability is achieved in selective security model. We also propose a new attribute based signcryption (ABSC) scheme for LSSS-realizable access structures utilizing only 6 pairings and making the ciphertext size constant. Our scheme is significantly more efficient than existing ABSC schemes. While the secret key size increases by a factor of number of attributes used in the system, the number of pairing evaluations is reduced to constant. Our protocol achieves (a) ciphertext indistinguishability under adaptive chosen ciphertext attacks assuming the hardness of decisional Bilinear Diffie-Hellman Exponent problem, (b) existential unforgeability under adaptive chosen message attack assuming the hardness of computational Diffie-Hellman Exponent problem and (c) strong unforgeability against insider adversary. The security proofs are in selective security model without using any random oracle. In addition, our ABSC achieves public verifiability of the ciphertext, enabling any party to verify the integrity and validity of the ciphertext.