Abstract
The purpose of this master's project is to study different probabilistic cryptography schemes. The older probabilistic schemes, Goldwasser-Micali and Blum-Goldwasser, will only be covered briefly for a historical perspective. Several new and promising schemes have appeared in the last 7 years, generating interest. I will be examining the Paillier and Damgard-Jurik schemes in depth. This report explains the mathematics behind the schemes along with their inherent benefits, while also suggesting some potential uses. Details are given on how I optimized the algorithms, with special emphasis on using the Chinese Remainder Theorem (CRT) in the Damgard-Jurik algorithm as well as the other algorithms. One of the main benefits these schemes posses is the additively homomorphic property. I explain the homomorphic properties in the description of the schemes and give an overview of these properties in Appendix A. I create software based in the Java Cryptography Extension (JCE) that is used to do a comparative study. This includes a simple message passing program for encrypted text. I create my own implementations of Paillier, Damgard-Jurik, and a variation of Paillier's scheme as a Provider using the JCE. These implementations use the CRT along with other methods to increase performance and create optimized algorithms. The implementations are plugged into the message passing program with an implementation of RSA from another Provider. A comparative study of the timings of these three schemes is done to show which one performs better in different circumstances. Conclusions are drawn based on the results of the tests and my final opinions are stated.
Publication Date
2006
Document Type
Master's Project
Student Type
Graduate
Department, Program, or Center
Computer Science (GCCIS)
Advisor
Radziszowski, Stanislaw
Advisor/Committee Member
Homan, Christopher
Advisor/Committee Member
Etlinger, Henry
Recommended Citation
Richardson, Kert, "Progress on probabilistic encryption schemes" (2006). Thesis. Rochester Institute of Technology. Accessed from
https://repository.rit.edu/theses/6919
Campus
RIT – Main Campus
Comments
Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2013.