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This list will undergo constant updates over the next couple of days.


Theory:

1) Computationally Secure (Single Database) Private Information Retrieval Schemes and 
Homomorphic Encryption. 

References: 
a) http://crypto.stanford.edu/~dabo/courses/cs355_fall07/pir.pdf 

2) A survey of circular security of  encryption schemes.
(OPTIONAL) OPEN PROBLEM: Prove (or disprove) the circular security of any 
of the existing homomorphic encryption schemes.

3) Information-Theoretically Secure Garbled Circuit Constructions
(for Boolean Formulas, Logspace computations), and Negative Results.
(OPTIONAL) OPEN PROBLEM: Show such constructions for circuits outside
Logspace (or prove impossibility.)

4) Succinct Non-interactive Argument (SNARG) Systems: Constructions and Impossibility Results.

References:
a) Impossibility: http://eprint.iacr.org/2010/610
b) Constructions: http://eprint.iacr.org/2011/443.pdf  


Implementation:


1) Implementation of a simple Spam Filtering Algorithm 
(say, using the Naive Bayes classifier), and performance
benchmarks. 

References:
a) HELib: https://github.com/shaih/HElib

2) Implementing the Gentry-Sahai-Waters'13 + Brakerski-Vaikuntanathan'13
FHE schemes and performance benchmarks.

References:
a) http://eprint.iacr.org/2013/340
b) http://eprint.iacr.org/2013/541