Publicly Evaluable Pseudorandom Functions and Its Applications
Publicly Evaluable Pseudorandom Functions and Its Applications
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可公开评估的伪随机函数及其应用
DOI：
10.1007/978-3-319-10879-7_8
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Yu Chen and Zongyang Zhang
中科院分区：
文献类型：
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作者：
Yu Chen;Qiong Huang and Zongyang Zhang;Yu Chen and Zongyang Zhang
本文提出了可公开赋值的伪随机函数（PEPRF）的概念，它可以看作是标准伪随机函数（PRF）在公钥环境下的对应物。简单地说，PEPRF是在域X上定义的，域X包含与硬关系相关联的语言L，并且每个秘密密钥与公钥相关联。对于任何情况，除了使用作为标准的PRF来计算Fsk（x）之外，还可以使用，x和一个空值来计算Fsk（x）。我们考虑两个安全概念的PEPRF。基本的一个是弱伪随机性，它规定PEPRF在均匀随机选择的输入上不能与真实的随机函数区分开。加强的一个是自适应弱伪随机性，它要求PEPRF保持弱伪随机，即使对手被赋予自适应访问评估预言。我们进行了形式化的研究PEPRFs，专注于应用，建设和extensions. ESTA我们展示了如何构建选择明文安全（CPA）和选择密文安全（CCA）公钥加密（PKE）计划（自适应）PEPRFs。这种构造是简单的，黑箱的，并且允许直接证明安全性。我们提供的证据表明，（自适应）PEPRFs存在，从内射陷门函数，哈希证明系统，可提取哈希证明系统，以及从可穿孔的PRFs与程序obfuscation.<$PSPRFs的建设，我们介绍的概念公开采样的PRFs（PSPRFs），这是一个放松的PEPRFs，但仍然意味着PKE。我们表明（自适应）PSPRFs隐含（自适应）陷门关系。这有助于我们统一和澄清许多PKE计划从看似无关的一般假设和范式下的概念PSPRFs. ESTA我们探索类似的扩展最近出现的约束PRFs，并介绍了公开评估的约束PRFs的概念，作为一个直接的应用程序，这意味着基于属性的加密。ESTA我们提出了一个扭曲的PEPRFs，我们称之为公开评估和可验证的功能（PEVF）。与PEPRF相比，PEVF具有一个额外的有前途的属性，称为公共可验证性，而最好的安全性则会降低到不可预测性。我们证明了PEVF的适用性，提出了一个简单的建设“散列和签名”的签名，无论是在随机预言机模型和标准模型。
We put forth the notion ofpublicly evaluablepseudorandom functions (PEPRFs), which can be viewed as a counterpart of standard pseudorandom functions (PRFs) in the public-key setting. Briefly, PEPRFs are defined over domainXcontaining a languageLassociated with a hard relation, and each secret keyis associated with a public key. For any, in addition to evaluate Fsk(x) usingas standard PRFs, one is also able to evaluate Fsk(x) with,xand a witnesswfor. We consider two security notions for PEPRFs. The basic one is weak pseudorandomness which stipulates a PEPRF cannot be distinguished from a real random function on uniformly random chosen inputs. The strengthened one is adaptive weak pseudorandomness which requires a PEPRF remains weak pseudorandom even when an adversary is given adaptive access to an evaluation oracle. We conduct a formal study of PEPRFs, focusing on applications, constructions, and extensions.∙ We show how to construct chosen-plaintext secure (CPA) and chosen-ciphertext secure (CCA) public-key encryption (PKE) schemes from (adaptive) PEPRFs. The construction is simple, black-box, and admits a direct proof of security. We provide evidence that (adaptive) PEPRFs exist by showing constructions from injective trapdoor functions, hash proof systems, extractable hash proof systems, as well as a construction from puncturable PRFs with program obfuscation.∙ We introduce the notion of publicly sampleable PRFs (PSPRFs), which is a relaxation of PEPRFs, but nonetheless imply PKE. We show (adaptive) PSPRFs are implied by (adaptive) trapdoor relations. This helps us to unify and clarify many PKE schemes from seemingly unrelated general assumptions and paradigms under the notion of PSPRFs.∙ We explore similar extension on recently emerging constrained PRFs, and introduce the notion of publicly evaluable constrained PRFs, which, as an immediate application, implies attribute-based encryption.∙ We propose a twist on PEPRFs, which we call publicly evaluable and verifiable functions (PEVFs). Compared to PEPRFs, PEVFs have an additional promising property named public verifiability while the best possible security degrades to unpredictability. We justify the applicability of PEVFs by presenting a simple construction of “hash-and-sign” signatures, both in the random oracle model and the standard model.