An In-Depth Study of Homomorphic Encryption in Cryptography

在今天的数字时代？S，联邦和商业日常运营的几乎所有方面都是基于网络的。这种对网络基础设施的严重依赖需要安全，因为没有安全，现代网络很容易受到内部和外部的攻击。该项目将提高我们的知识水平和我们对保障网络基础设施安全所需的一些基本加密任务的了解。加密任务的效率通常根据计算负载、所需的通信带宽和所需的交互轮数来衡量。这项研究的目标包括研究允许对私钥的函数进行加密的公钥加密方案。另一个目标是开始对具有附加代数属性的公钥加密方案进行广泛的研究，这些公钥加密方案允许组合密文(而不知道解密)。这项研究工作的另一个目标是研究新的技术，以加快执行密码任务所涉及的计算。这一努力将资助新学生加入研究计划，并将通过教育--包括对少数族裔学生、安全专业人员和顾问的教育--进行推广努力。此外，这个项目的结果将被整合到加州大学洛杉矶分校研究生和本科生的课程中。

In today?s digital age almost all aspects of both federal and commercial day-to-day operations are cyber-based. This heavy reliance on cyber-infrastructure requires security, as without security modern networks are susceptible to both internal and external attacks. This project will result in the advancement of our state of knowledge and our understanding of a number of fundamental cryptographic tasks needed for securing cyber-infrastructure. The efficiency of cryptographic tasks is typically measured in terms of computational load, communication bandwidth needed, and the number of rounds of interaction required. The goals for this research include a study of public key encryption schemes that allow one to encrypt functions of private keys. Another goal is to embark on a broad study of public key encryption schemes with additional algebraic properties that allow combining cyphertexts (without knowing the decryption). Yet another goal of this research effort is to study new techniques for speeding up the computation involved in performing cryptographic tasks. This effort will sponsor new students to join the research program, and it will exercise outreach efforts through education?including education for minority student and security professionals and consultants. Additionally, the results of this project will be integrated into the course curriculum at UCLA at both the graduate and undergraduate levels.