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COXETER
LECTURE SERIES
October 28, 2015 at 4:00 p.m.
October 29,
2015 at 4:00 p.m.
October 30,
2015 at 4:00 p.m.
Fields Institute, Room 230
VICTOR SHOUP
Courant Institute
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October
28, 4:00 p.m.
Computing on encrypted data and fast polynomial arithmetic
In this talk, I will give a general
introduction to the notion of fully homomorphic encryption, including
some history, motivation, and some of the basic ideas behind the
design and implementation of such a scheme. Fully homomorphic
encryption allows one to carry out arbitrary computations on encrypted
data. For example, with it, users can store sensitive data "in
the cloud" in encrypted form, and cloud servers can compute
statistics on that data on behalf of the user, without any of
the user's data being exposed to the cloud. Realizing such a scheme
had been an open problem for many years. In a breakthrough in
2009, Craig Gentry showed that such schemes can be constructed.
Initial designs of such schemes were hopelessly impractical; however,
we are now making great strides towards practical implementations.
Making such a scheme at all practical requires a great deal of
engineering, including algorithms for polynomial arithmetic on
huge polynomials, and also the application of ideas from the theory
of cyclotomic fields.
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October
29, 4:00 p.m.
Fully homomorphic encryption: computing on encrypted data
with helib
This talk will start where the first
talk left off. I will dive more deeply into the algorithms at
the heart of our implementation of fully homomorphic encryption.
In particular, I will discuss algorithms for fundamental operations
on encrypted data, such as computing linear maps.
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October
30, 4:00 p.m.
NTL: a library for doing number theory
NTL is a high-performance C++ library for doing arithmetic on
polynomial over various rings (integers and finite fields), as
well as a number of other algebraic structures. I will discuss
the history of NTL, as well as some of the basic elements of its
design and the algorithms it employs. I will also discuss recent
work on making NTL exploit multicore computer architectures.
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About Victor Shoup
Victor Shoup is a professor of Computer Science at New York University.
His main areas of research are cryptography and number-theoretic algorithms.
He is the co-inventor of the Cramer-Shoup cryptosystem, the first practical
public-key encryption scheme that is provably secure in the strongest sense.
He is also the developer of NTL, a popular high-performance library for
doing computations over a variety of rings.
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