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-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)