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 ... more >>>

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 ... more >>>

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 ... more >>>

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 >>>

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 >>>

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 >>>

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 >>>