Faculty Advisor

Martin, William J.


Suppose I give you a massively overdetermined yet consistent system of linear equations Ax = b over a finite ring, but I change a few of the values of b before showing it to you. Can you still solve for x? This is called the Learning With Errors problem, and it was introduced by Regev in 2009, who showed that it is hard on average. Today it is used in many homomorphic encryption schemes. Such schemes allow anyone to run computations on encrypted data without being able to learn what the data are. In this paper, I look at ways to exploit poor randomness in Learning With Errors. For extremely sparse noise models, I give polynomial-time solutions to the Learning With Errors problem.


Worcester Polytechnic Institute

Date Accepted

April 2016


Mathematical Sciences

Project Type

Major Qualifying Project



Advisor Department

Mathematical Sciences