### Targeted Homomorphic Attribute Based Encryption

Zvika Brakerski, David Cash, Rotem Tsabary, and Hoeteck Wee

##### Abstract

In (key-policy) attribute based encryption (ABE), messages are encrypted respective to attributes $x$, and keys are generated respective to policy functions $f$. The ciphertext is decryptable by a key only if $f(x)=0$. Adding homomorphic capabilities to ABE is a long standing open problem, with current techniques only allowing compact homomorphic evaluation on ciphertext respective to the same $x$. Recent advances in the study of multi-key FHE also allow cross-attribute homomorphism with ciphertext size growing (quadratically) with the number of input ciphertexts. We present an ABE scheme where homomorphic operations can be performed compactly across attributes. Of course, decrypting the resulting ciphertext needs to be done with a key respective to a policy $f$ with $f(x_i)=0$ for all attributes involved in the computation. In our scheme, the target policy $f$ needs to be known to the evaluator, we call this targeted homomorphism. Our scheme is secure under the polynomial hardness of learning with errors (LWE) with sub-exponential modulus-to-noise ratio. We present a second scheme where there needs not be a single target policy. Instead, the decryptor only needs a set of keys representing policies $f_j$ s.t.\ for any attribute $x_i$ there exists $f_j$ with $f_j(x_i)=0$. In this scheme, the ciphertext size grows (quadratically) with the size of the set of policies (and is still independent of the number of inputs or attributes). Again, the target set of policies needs to be known at evaluation time. This latter scheme is secure in the random oracle model under the polynomial hardness of LWE with sub-exponential noise ratio.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
attribute-based encryptionfully homomorphic encryptionattribute-based FHEhomomorphic ABE
Contact author(s)
rotem ts0 @ gmail com
History
Short URL
https://ia.cr/2016/691

CC BY

BibTeX

@misc{cryptoeprint:2016/691,
author = {Zvika Brakerski and David Cash and Rotem Tsabary and Hoeteck Wee},
title = {Targeted Homomorphic Attribute Based Encryption},
howpublished = {Cryptology ePrint Archive, Paper 2016/691},
year = {2016},
note = {\url{https://eprint.iacr.org/2016/691}},
url = {https://eprint.iacr.org/2016/691}
}

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