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Electronic Colloquium on Computational Complexity

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Reports tagged with homomorphic encryption:
TR01-057 | 15th August 2001
Boaz Barak, Oded Goldreich, Russell Impagliazzo, Steven Rudich, Amit Sahai, Salil Vadhan, Ke Yang

On the (Im)possibility of Obfuscating Programs

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 >>>

TR07-022 | 20th February 2007
Rafail Ostrovsky, William Skeith

Algebraic Lower Bounds for Computing on Encrypted Data

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 >>>

TR10-146 | 21st September 2010
Ron Rothblum

Homomorphic Encryption: from Private-Key to Public-Key

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 >>>

TR12-156 | 12th November 2012
Andrej Bogdanov, Chin Ho Lee

Limits of provable security for homomorphic encryption

Revisions: 1

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 >>>

TR12-157 | 12th November 2012
Andrej Bogdanov, Chin Ho Lee

On the depth complexity of homomorphic encryption schemes

Revisions: 2

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 >>>

TR14-106 | 9th August 2014
Craig Gentry

Computing on the edge of chaos: Structure and randomness in encrypted computation

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 >>>

TR15-061 | 14th April 2015
Benny Applebaum, Jonathan Avron, Christina Brzuska

Arithmetic Cryptography

Revisions: 1

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 >>>

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