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.
Normal 0 false false false EN-US JA X-NONE Project Outcomes Report for NSF grant 0830803: "An In-Depth Study of Homomorphic Encryption in Cryptography" PI’s: Rafail Ostrovsky, Amit Sahai This project covered a number of research topics spanning cryptography, with an overall focus on developing and studying cryptographic protocols. Over the course of this grant, more than 10 current and former Ph.D. students, 5 postdoctoral fellows, and 6 outside researchers contributed to this research. This research contributed to the publication of more than 40 original research publications. Here, we highlight just one contribution in the key area of research that of zero-knowledge proofs with additional security properties. Zero-Knowledge proofs is a fascinating and counter-intuitive notion: In a zero-knowledge proof, one entity, called the Prover, tries to convince another entity, called the Verifier, that some statement is true. If the statement really is true, then the Prover will succeed in convincing the Verifier. However, if the statement is false, the Prover should not be able to convince the Verifier to accept his proof. Finally, the most crucial and counter-intuitive property of zero-knowledge proofs is that even if the Prover succeeds in convincing the Verifier that the statement is true, the Verifier should not learn anything about why the statement is true. For applications to cryptography, the kind of statements that a Prover wants to prove concern secrets – and what makes zero-knowledge proofs so useful is that they allow a Prover to prove facts about his secrets without revealing them. Before our research under this grant, zero-knowledge proofs that a Prover could write down in a file would have allowed future advances in computing to eventually recover the secret from the written proof. In work published in the Journal of the ACM in 2012, the PIs, working with their former postdoctoral student Jens Groth, presented a detailed solution of constructing the first perfect zero-knowledge proofs that could be written once and for all, never revealing their secrets. This settled a question that had been open for 18 years at the time the PIs first devised their solution and lay the groundwork for the construction of ``lossy encryption’’ that proved a key building block for multiple follow-up discoveries. The mathematics of elliptic curves played a crucial role in our new technique for constructing zero-knowledge proofs. Jens Groth, Rafail Ostrovsky, Amit Sahai: New Techniques for Noninteractive Zero-Knowledge. J. ACM 59(3): 11 (2012)
