All reports by Author Craig Gentry:

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TR18-149
| 25th August 2018
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Craig Gentry, Charanjit Jutla#### Obfuscation using Tensor Products

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TR14-106
| 9th August 2014
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Craig Gentry#### Computing on the edge of chaos: Structure and randomness in encrypted computation

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TR14-105
| 9th August 2014
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Craig Gentry#### Noncommutative Determinant is Hard: A Simple Proof Using an Extension of Barrington’s Theorem

Comments: 1

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TR11-111
| 10th August 2011
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Zvika Brakerski, Craig Gentry, Vinod Vaikuntanathan#### Fully Homomorphic Encryption without Bootstrapping

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TR07-133
| 20th November 2007
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Craig Gentry, Chris Peikert, Vinod Vaikuntanathan#### Trapdoors for Hard Lattices and New Cryptographic Constructions

Craig Gentry, Charanjit Jutla

We describe obfuscation schemes for matrix-product branching programs that are purely algebraic and employ matrix algebra and tensor algebra over a finite field. In contrast to the obfuscation schemes of Garg et al (SICOM 2016) which were based on multilinear maps, these schemes do not use noisy encodings. We prove ... 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 >>>

Craig Gentry

We show that, for many noncommutative algebras A, the hardness of computing the determinant of matrices over A follows almost immediately from Barrington’s Theorem. Barrington showed how to express a NC1 circuit as a product program over any non-solvable group. We construct a simple matrix directly from Barrington’s product program ... more >>>

Zvika Brakerski, Craig Gentry, Vinod Vaikuntanathan

We present a radically new approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions. A central conceptual contribution in our work is a new way of constructing leveled fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits), {\em without Gentry's bootstrapping procedure}.

... more >>>Craig Gentry, Chris Peikert, Vinod Vaikuntanathan

We show how to construct a variety of ``trapdoor'' cryptographic tools

assuming the worst-case hardness of standard lattice problems (such as

approximating the shortest nonzero vector to within small factors).

The applications include trapdoor functions with \emph{preimage

sampling}, simple and efficient ``hash-and-sign'' digital signature

schemes, universally composable oblivious transfer, ...
more >>>