Ciphertext-Policy ABE for ${\mathsf{NC}}^1$ Circuits with Constant-Size Ciphertexts from Succinct LWE

Abstract

We construct a lattice-based ciphertext-policy attribute-based encryption (CP-ABE) scheme for ${\mathsf{NC}}^1$ access policies with constant-size ciphertexts. Let $\hat{I}»$ be the security parameter. For an ${\mathsf{NC}}^1$ circuit of depth $d$ and size $s$ on $\ell$-bit inputs, our scheme has the public-key and ciphertext sizes $O(1)$ (independent of $d$), and secret-key size $O(\ell )$, where the $O(\cdot )$ hides $\mathrm{poly}(\hat{I}»)$ factors. As an application, we obtain a broadcast encryption scheme for $N$ users with ciphertext size $\mathrm{poly}(\hat{I}»)$ independent of $\log N$ and key sizes $\mathrm{poly}(\hat{I}»,\log N)$. Our construction is selectively secure in the standard model under the $\mathrm{poly}(\hat{I}»)$-succinct LWE assumption introduced by Wee (CRYPTO~2024).

37 pages