Attribute-Based Access Control for Inner Product Functional Encryption from LWE

Abstract

The notion of functional encryption (FE) was proposed as a generalization of plain public-key encryption to enable a much more fine-grained handling of encrypted data, with advanced applications such as cloud computing, multi-party computations, obfuscating circuits or Turing machines. While FE for general circuits or Turing machines gives a natural instantiation of the many cryptographic primitives, existing FE schemes are based on indistinguishability obfuscation or multilinear maps which either rely on new computational hardness assumptions or heuristically claimed to be secure. In this work, we present new techniques directly yielding FE for inner product functionality where secret-keys provide access control via polynomial-size bounded-depth circuits. More specifically, we encrypt messages with respect to attributes and embed policy circuits into secret-keys so that a restricted class of receivers would be able to learn certain property about the messages. Recently, many inner product FE schemes were proposed. However, none of them uses a general circuit as an access structure. Our main contribution is designing the first construction for an attribute-based FE scheme in key-policy setting for inner products from well-studied Learning With Errors (\(\mathsf {LWE}\)) assumption. Our construction takes inspiration from the attribute-based encryption of Boneh et al. from Eurocrypt 2014 and the inner product functional encryption of Agrawal et al. from Crypto 2016. The scheme is proved in a stronger setting where the adversary is allowed to ask secret-keys that can decrypt the challenge ciphertext. Doing so requires a careful setting of parameters for handling the noise in ciphertexts to enable correct decryption. Another main advantage of our scheme is that the size of ciphertexts and secret-keys depends on the depth of the circuits rather than its size. Additionally, we extend our construction in a much desirable multi-input variant where secret-keys are associated with multiple policies subject to different encryption slots. This enhances the applicability of the scheme with finer access control.