We propose simple generic constructions of succinct functional encryption. Our key tool is strong exponentially efficient indistinguishability obfuscator (SXIO), which is the same as indistinguishability obfuscator (IO) except that the size of an obfuscated circuit and the running time of an obfuscator are slightly smaller than that of a brute-force canonicalizer that outputs the entire truth table of a circuit to be obfuscated. A “compression factor” of SXIO indicates how much SXIO compresses the brute-force canonicalizer. In this study, we propose a significantly simple framework to construct succinct functional encryption via SXIO and show that SXIO is powerful enough to achieve cutting-edge cryptography. In particular, we propose the following constructions:

• Single-key weakly succinct secret-key functional encryption (SKFE) is constructed from SXIO (even with a bad compression factor) and one-way functions.

• Single-key weakly succinct public-key functional encryption (PKFE) is constructed from SXIO with a good compression factor and public-key encryption.

• Single-key weakly succinct PKFE is constructed from SXIO (even with a bad compression factor) and identity-based encryption.

Our new framework has side benefits. Our constructions do not rely on any number theoretic or lattice assumptions such as decisional Diffie–Hellman and learning with errors assumptions. Moreover, all security reductions incur only polynomial security loss. Known constructions of weakly succinct SKFE or PKFE from SXIO with polynomial security loss rely on number theoretic or lattice assumptions. As corollaries of our results, relationships among SXIO, a few variants of SKFE, and a variant of randomized encoding are discovered.

我们提出简洁功能加密的简单通用构造。我们的主要工具是强呈指数有效不可分辨混淆（SXIO），其是相同的不可分辨混淆（IO），除了模糊化的电路的尺寸和模糊处理程序的运行时间是稍微比蛮力canonicalizer该小输出要混淆的电路的整个真值表。SXIO的“压缩因子”指示SXIO压缩强力规范化器的程度。在这项研究中，我们提出了一个非常简单的框架来通过SXIO构建简洁的功能加密，并表明SXIO足够强大，可以实现先进的加密技术。特别是，我们提出以下构造：

• 单密钥弱简洁秘密密钥功能加密（SKFE）是由SXIO（即使压缩系数较差）和单向功能构造而成的。

• 单密钥弱简洁的公共密钥功能加密（PKFE）是由具有良好压缩因子和公共密钥加密的SXIO构建的。

• 单键弱简洁PKFE由SXIO（即使压缩系数不佳）和基于身份的加密构成。

我们的新框架有一些附带好处。我们的构造不依赖任何数字理论或晶格假设，例如决策性Diffie-Hellman和有错误学习的假设。而且，所有安全性降低仅引起多项式安全性损失。来自SXIO的，具有多项式安全损失的弱简洁SKFE或PKFE的已知构造依赖于数论或晶格假设。作为我们结果的推论，发现了SXIO，SKFE的一些变体和随机编码的变体之间的关系。