We construct the first decentralized multi-authority attribute-based encryption (MA-ABE) scheme for a non-trivial class of access policies whose security is based (in the random oracle model) solely on the Learning With Errors (LWE) assumption. The supported access policies are ones described by DNF formulas. All previous constructions of MA-ABE schemes supporting any non-trivial class of access policies were proven secure (in the random oracle model) assuming various assumptions on bilinear maps.

In our system, any party can become an authority and there is no requirement for any global coordination other than the creation of an initial set of common reference parameters. A party can simply act as a standard ABE authority by creating a public key and issuing private keys to different users that reflect their attributes. A user can encrypt data in terms of any DNF formulas over attributes issued from any chosen set of authorities. Finally, our system does not require any central authority. In terms of efficiency, when instantiating the scheme with a global bound s on the size of access policies, the sizes of public keys, secret keys, and ciphertexts, all grow with s.

Technically, we develop new tools for building ciphertext-policy ABE (CP-ABE) schemes using LWE. Along the way, we construct the first provably secure CP-ABE scheme supporting access policies in NC1 that avoids the generic universal-circuit-based key-policy to ciphertext-policy transformation. In particular, our construction relies on linear secret sharing schemes with new properties and in some sense is more similar to CP-ABE schemes that rely on bilinear maps. While our CP-ABE construction is not more efficient than existing ones, it is conceptually intriguing and further we show how to extend it to get the MA-ABE scheme described above.