Boaz Barak, Oded Goldreich, Russell Impagliazzo, Steven Rudich, Amit Sahai, Salil Vadhan, Ke Yang

Informally, an <i>obfuscator</i> <b>O</b> is an (efficient, probabilistic)

"compiler" that takes as input a program (or circuit) <b>P</b> and

produces a new program <b>O(P)</b> that has the same functionality as <b>P</b>

yet is "unintelligible" in some sense. Obfuscators, if they exist,

would have a wide variety of cryptographic ...
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Rafail Ostrovsky, William Skeith

In cryptography, there has been tremendous success in building

primitives out of homomorphic semantically-secure encryption

schemes, using homomorphic properties in a black-box way. A few

notable examples of such primitives include items like private

information retrieval schemes and collision-resistant hash functions. In this paper, we illustrate a general

methodology for ...
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Ron Rothblum

We show that any private-key encryption scheme that is weakly

homomorphic with respect to addition modulo 2, can be transformed

into a public-key encryption scheme. The homomorphic feature

referred to is a minimalistic one; that is, the length of a

homomorphically generated encryption should be independent of the

number of ...
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Andrej Bogdanov, Chin Ho Lee

We show that public-key bit encryption schemes which support weak homomorphic evaluation of parity or majority cannot be proved message indistinguishable beyond AM intersect coAM via general (adaptive) reductions, and beyond statistical zero-knowledge via reductions of constant query complexity.

Previous works on the limitation of reductions for proving security of ... more >>>

Andrej Bogdanov, Chin Ho Lee

We show that secure homomorphic evaluation of any non-trivial functionality of sufficiently many inputs with respect to any CPA secure encryption scheme cannot be implemented by constant depth, polynomial size circuits, i.e. in the class AC0. In contrast, we observe that certain previously studied encryption schemes (with quasipolynomial security) can ... more >>>

Craig Gentry

This survey, aimed mainly at mathematicians rather than practitioners, covers recent developments in homomorphic encryption (computing on encrypted data) and program obfuscation (generating encrypted but functional programs). Current schemes for encrypted computation all use essentially the same "noisy" approach: they encrypt via a noisy encoding of the message, they decrypt ... more >>>

Benny Applebaum, Jonathan Avron, Christina Brzuska

We study the possibility of computing cryptographic primitives in a fully-black-box arithmetic model over a finite field F. In this model, the input to a cryptographic primitive (e.g., encryption scheme) is given as a sequence of field elements, the honest parties are implemented by arithmetic circuits which make only a ... more >>>