We construct a lattice-based ciphertext-policy attribute-based encryption (CP-ABE) scheme for $\mathsf{NC}^1$ access policies with constant-size ciphertexts. Let $λ$ 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 $\operatorname{poly}(λ)$ factors. As an application, we obtain a broadcast encryption scheme for $N$ users with ciphertext size $\operatorname{poly}(λ)$ independent of $\log N$ and key sizes $\operatorname{poly}(λ,\log N)$. Our construction is selectively secure in the standard model under the $\operatorname{poly}(λ)$-succinct LWE assumption introduced by Wee (CRYPTO~2024).

翻译：我们构造了一种基于格的密文策略属性基加密方案，该方案支持$\mathsf{NC}^1$访问策略，且具有恒定大小的密文。令$λ$为安全参数。对于一个深度为$d$、规模为$s$、输入为$\ell$比特的$\mathsf{NC}^1$电路，本方案的公钥和密文大小为$O(1)$（与$d$无关），私钥大小为$O(\ell)$，其中$O(\cdot)$隐藏了$\operatorname{poly}(λ)$因子。作为应用，我们获得了一个支持$N$个用户的广播加密方案，其密文大小为$\operatorname{poly}(λ)$（与$\log N$无关），密钥大小为$\operatorname{poly}(λ,\log N)$。我们的构造在标准模型下，基于Wee（CRYPTO~2024）提出的$\operatorname{poly}(λ)$-简洁LWE假设，具有选择性安全性。