An In-Depth Study of Homomorphic Encryption in Cryptography

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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.