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5.0 Conclusions and Recommendations
The PROCEED AHEAD team has delivered outstanding results in just the first half (two years)
of the intended four year project. Our results spanned from both fundamental theoretical
contributions to the development of Fully Homomorphic Encryption (FHE), special forms of
FHE, better lattice design, through applications such as delegation of computations and
understanding of the underlyings of multiparty computations, to implementations and
optimizations of FHE.
There lies significant opportunity to build upon our work from the first two years of the
PROCEED AHEAD project including additional aspects of computation delegation. There is
also an opening to apply our prototype system for performing statistical analysis on large scale
data computing the mean and covariance of multivariate data and performing linear regression
over encrypted datasets. Also, the Homomorphic Encryption (HE) software library[18] requires
the cooperation from PROCEED program partners and the cryptographic research community at
large to advance it from its current "proof of concept" state into a fully homomorphic encryption
scheme applicable to real world tasks such as network guards and other computations on
encrypted data such as curve fitting (e.g., least-squares fit).
Even with the major advances in the state of HE over the last few years, both the size of HE
ciphertext and the complexity of computing them remain quite high. An obvious direction for
future work is to find additional optimizations to reduce this overhead further. One direction
which was not explored but seems to have large potential, is finding a cheaper method to replace
Gentry's bootstrapping technique. Namely, it is still plausible that we can reduce the noise in the
ciphertext by applying a cheaper transformation than full homomorphic decryption.
The team has worked intensely on the AHEAD project, collaborating with other participants
within the PROCEED program, and has delivered results in a pace that even surprised us! IBM
has enjoyed working on the project and will take leave (resulting from limitation of funds) while
Stanford and UCSD continue to work within the PROCEED program.
Approved for Public Release; Distribution Unlimited.
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