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Secure Computation on Encrypted Data

Periodic Reporting for period 4 - aSCEND (Secure Computation on Encrypted Data)

Reporting period: 2019-12-01 to 2021-05-31

Recent trends in computing have prompted users and organizations to
store an increasingly large amount of sensitive data at third party
locations in the cloud outside of their direct control. Storing data
remotely poses an acute security threat as these data are outside our
control and could potentially be accessed by untrusted parties.
Indeed, the reality of these threats have been borne out by the
Snowden leaks and hundreds of data breaches each year. In order to
protect our data, we will need to encrypt it.

Functional encryption is a novel paradigm for public-key encryption
that enables both fine-grained access control and selective
computation on encrypted data, as is necessary to protect big, complex
data in the cloud. Functional encryption also enables searches on
encrypted travel records and surveillance video as well as medical
studies on encrypted medical records in a privacy-preserving manner;
we can give out restricted secret keys that reveal only the
outcome of specific searches and tests. These mechanisms allow us to
maintain public safety without compromising on civil liberties, and to
facilitate medical break-throughs without compromising on individual

The goals of the aSCEND project are (i) to design pairing and
lattice-based functional encryption that are more *efficient* and
ultimately viable in practice; and (ii) to obtain a richer
understanding of *expressive* functional encryption schemes and to push
the boundaries from encrypting data to encrypting software. My
long-term vision is the ubiquitous use of functional encryption to
secure our data and our computation, just as public-key encryption is
widely used today to secure our communication. Realizing this vision
requires new advances in the foundations of functional encryption,
which is the target of this project.
We made significant progress in constructing both efficient and
expressive attribute-based and functional encryption schemes. We
highlight three results: (i) functional encryption for all circuits
for a weaker one-sided security notion; (ii) fully automated methods
for proving security of very efficient pairing-based attribute-based
encryption schemes in an idealized model; (iii) efficient
pairing-based functional encryption for inner product in the
multi-input setting, where the decryptor is able to compute a weighted
average of values encrypted across multiple ciphertexts.

The study of functional encryption has had a huge scientific impact on
the field of cryptography, thanks to the development of new and
powerful tools and techniques. Indeed, we discovered new applications
of techniques we developed to a variety of cryptographic primitives
such as public-key encryption scheme secure against chosen-ciphertext
attacks (CCA) and fully homomorphic encryption.
We plan to continue exploring constructions of efficient and
expressive functional encryption schemes, as well as to discover new
applications of techniques used in our constructions to other
cryptographic primitives.