Compact Attribute-Based Encryption and Signcryption for General Circuits from Multilinear Maps∗

Abstract. Designing attribute-based systems supporting highly expressive access policies has been one of the principal focus of research in attribute-based cryptography. While attribute-based encryp-tion (ABE) enables fine-grained access control over encrypted data in a multi-user environment, attribute-based signature (ABS) provides a powerful tool for preserving signer anonymity. Attribute-based signcryption (ABSC), on the other hand, is a combination of ABE and ABS into a unified cost-effective primitive. In this paper, we start by presenting a key-policy ABE supporting general polynomial-size circuit realizable decryption policies and featuring compactness. More specifically, our ABE construction exhibits short ciphertexts and shorter decryption keys compared to existing similar works. We then proceed to design a key-policy ABSC scheme which enjoys several interesting properties that were never achievable before. It supports arbitrary polynomial-size circuits, thereby handles highly sophisticated control over signing and decryption rights. Besides, it generates short ciphertext as well. Our ABE construction employs multilinear map of level n + l + 1, while that used for our ABSC scheme has level n + n ′ + l + 1, where n, n′, and l represent respectively the input length of decryption policy circuits, input size of signing policy circuits, and depth of both kinds of circuits. Selective security of our constructions are proven in the standard model under the Multilinear Decisional Diffie-Hellman and Multilinear Computational Diffie-Hellman assumptions which are standard complexity assumptions in the multilinear map setting. Our key-policy construc-tions can be converted to the corresponding ciphertext-policy variants achieving short ciphertext by utilizing the technique of universal circuits