## Cryptology ePrint Archive: Report 2013/669

**Attribute-Based Encryption for Arithmetic Circuits**

*Dan Boneh and Valeria Nikolaenko and Gil Segev*

**Abstract: **We present an Attribute Based Encryption system where access policies are expressed as polynomial size arithmetic circuits. We prove security against arbitrary collusions of users based on the learning with errors problem on integer lattices. The system has two additional useful properties: first, it naturally handles arithmetic circuits with arbitrary fan-in (and fan-out) gates. Second, secret keys are much shorter than in previous schemes: secret key size is proportional to the depth of the circuit where as in previous constructions the key size was proportional to the number of gates or wires in the circuit. The system is well suited for environments where access policies are naturally expressed as arithmetic circuits as is the case when policies capture statistical properties of the data or depend on arithmetic transformations of the data. The system also provides complete key delegation capabilities.

**Category / Keywords: **Attribute Based Encryption, ABE, Key-Homomorphic Public Key Encryption, arithmetic circuits, selective security, learning with errors, LWE, lattices

**Date: **received 18 Oct 2013, last revised 21 Oct 2013

**Contact author: **valerini at stanford edu

**Available format(s): **PDF | BibTeX Citation

**Version: **20131024:083232 (All versions of this report)

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