Inner product functional encryption (IPFE) is one class of functional encryption supporting only inner product functionality. All previous IPFE schemes are bounded schemes, meaning that the vector length that can be handled in the scheme is fixed in the setup phase. In this paper, we propose the first unbounded IPFE schemes, in which we do not have to fix the lengths of vectors in the setup phase and can handle (a priori) unbounded polynomial lengths of vectors. Our first scheme is private-key based and fully function hiding. That is, secret keys hide the information of the associated function. Our second scheme is public-key based and provides adaptive security in the indistinguishability based security definition. Both our schemes are based on SXDH, which is a well-studied standard assumption, and secure in the standard model. Furthermore, our schemes are quite efficient, incurring an efficiency loss by only a small constant factor from previous bounded function hiding schemes.

中文翻译：

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双线性映射的无穷内积函数加密

产品内部功能加密（IPFE）是仅支持内部产品功能的一类功能加密。所有先前的IPFE方案都是有界方案，这意味着可以在方案中处理的向量长度在设置阶段是固定的。在本文中，我们提出了第一个无边界IPFE方案，其中我们不必在设置阶段固定向量的长度，并且可以处理（先验）向量的无穷多项式长度。我们的第一个方案是基于私钥和全功能隐藏。即，秘密密钥隐藏了相关功能的信息。我们的第二个方案是基于公钥的，并在基于不可区分性的安全性定义中提供了自适应安全性。我们的两种方案均基于SXDH，这是经过充分研究的标准假设，并且在标准模型中安全。此外，