On Foundations of Protecting Computations

Information technology systems have become indispensable to uphold our
way of living, our economy and our safety. Failure of these systems can have
devastating effects. Consequently, securing these systems against malicious
intentions deserves our utmost attention.

Cryptography provides the necessary foundations for that purpose. In
particular, it provides a set of building blocks which allow to secure larger
information systems. Furthermore, cryptography develops concepts and tech-
niques towards realizing these building blocks. The protection of computations
is one invaluable concept for cryptography which paves the way towards
realizing a multitude of cryptographic tools. In this thesis, we contribute to
this concept of protecting computations in several ways.

Protecting computations of probabilistic programs. An indis-
tinguishability obfuscator (IO) compiles (deterministic) code such that it
becomes provably unintelligible. This can be viewed as the ultimate way
to protect (deterministic) computations. Due to very recent research, such
obfuscators enjoy plausible candidate constructions.
In certain settings, however, it is necessary to protect probabilistic com-
... mehr
putations. The only known construction of an obfuscator for probabilistic
programs is due to Canetti, Lin, Tessaro, and Vaikuntanathan, TCC, 2015 and
requires an indistinguishability obfuscator which satisfies extreme security
guarantees. We improve this construction and thereby reduce the require-
ments on the security of the underlying indistinguishability obfuscator.
(Agrikola, Couteau, and Hofheinz, PKC, 2020)

Protecting computations in cryptographic groups. To facilitate
the analysis of building blocks which are based on cryptographic groups,
these groups are often overidealized such that computations in the group
are protected from the outside. Using such overidealizations allows to prove
building blocks secure which are sometimes beyond the reach of standard
model techniques. However, these overidealizations are subject to certain
impossibility results. Recently, Fuchsbauer, Kiltz, and Loss, CRYPTO, 2018
introduced the algebraic group model (AGM) as a relaxation which is closer
to the standard model but in several aspects preserves the power of said
overidealizations. However, their model still suffers from implausibilities.
We develop a framework which allows to transport several security proofs
from the AGM into the standard model, thereby evading the above implausi-
bility results, and instantiate this framework using an indistinguishability
obfuscator.
(Agrikola, Hofheinz, and Kastner, EUROCRYPT, 2020)

Protecting computations using compression. Perfect compression
algorithms admit the property that the compressed distribution is truly
random leaving no room for any further compression. This property is
invaluable for several cryptographic applications such as “honey encryption”
or password-authenticated key exchange. However, perfect compression
algorithms only exist for a very small number of distributions. We relax the
notion of compression and rigorously study the resulting notion which we
call “pseudorandom encodings”. As a result, we identify various surprising
connections between seemingly unrelated areas of cryptography. Particularly,
we derive novel results for adaptively secure multi-party computation which
allows for protecting computations in distributed settings. Furthermore, we
instantiate the weakest version of pseudorandom encodings which suffices
for adaptively secure multi-party computation using an indistinguishability
obfuscator.
(Agrikola, Couteau, Ishai, Jarecki, and Sahai, TCC, 2020)