Circuit ABE with  \(\textsf{poly}(\text {depth},\lambda )\) -Sized Ciphertexts and Keys from Lattices

We present new lattice-based attribute-based encryption (ABE) and laconic function evaluation (LFE) schemes for circuits with sublinear ciphertext overhead. For depth d circuits over \(\ell \) -bit inputs, we obtain where \(O(\cdot )\) hides \(\textsf{poly}(d,\lambda )\) factors. The first two results achieve almost optimal ciphertext and secret key/digest sizes, up to the \(\textsf{poly}(d)\) dependencies. The security of our schemes relies on \(\ell \) -succinct LWE, a falsifiable assumption which is implied by evasive LWE. At the core of our results is a new technique for compressing LWE samples \(\textbf{s}(\textbf{A}-\textbf{x}\otimes \textbf{G})\) as well as the matrix \(\textbf{A}\) .