Efficient Polynomial Operations in the Shared-Coefficients Setting

• Published in: Lecture notes in computer science pp. 44 - 57
• Main Authors: Mohassel, Payman, Franklin, Matthew
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2006; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Applied sciences; Computer science; control theory; systems; Exact sciences and technology; Memory and file management (including protection and security); Memory organisation. Data processing; passive adversary; polynomial operations; privacy-preserving set operations; secure multi-party computation; Software; threshold homomorphic encryption; Data privacy; Public key; Polynomial interpolation; Public key cryptography; Greatest commun divisor; Computer security; Information theory
• ISBN: 9783540338512; 3540338519
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11745853_4

We study the design of efficient and private protocols for polynomial operations in the shared-coefficients setting. We propose efficient protocols for polynomial multiplication, division with remainder, polynomial interpolation, polynomial gcd, and a few other operations. All the protocols introduced in this paper are constant-round, and more efficient than the general MPC. The protocols are all composable, and can be combined to perform more complicated functionalities. We focus on using a threshold additively homomorphic public key scheme due to the applications of our protocols. But, our protocols can also be securely computed in the information-theoretic setting. Finally, we mention some applications of our protocols to privacy-preserving set-operations.