We present compact attribute-based encryption (ABE) schemes for NC1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textsf {NC}}^{1}$$\end{document} that are adaptively secure under the k-Lin assumption with polynomial security loss. Our KP-ABE scheme achieves ciphertext size that is linear in the attribute length and independent of the policy size even in the many-use setting, and we achieve an analogous efficiency guarantee for CP-ABE. This resolves the central open problem posed by Lewko and Waters (CRYPTO 2011). Previous adaptively secure constructions either impose an attribute “one-use restriction” (or the ciphertext size grows with the policy size) or require q-type assumptions.

中文翻译：

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来自 k-Lin 的 $${\textsf {NC}}^{1}$$ NC 1 的紧凑自适应安全 ABE

我们为 NC1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs } \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textsf {NC}}^{1}$$\end{document} 在 k-Lin 下自适应安全多项式安全损失的假设。我们的 KP-ABE 方案实现了与属性长度呈线性关系且与策略大小无关的密文大小，即使在多次使用的设置中，我们也为 CP-ABE 实现了类似的效率保证。这解决了 Lewko 和 Waters (CRYPTO 2011) 提出的中心开放问题。