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Our first system, which is the centerpiece of this paper, is an attribute-based encryption based on the learning with errors problem that supports functions f represented as arithmetic circuits with large fan-in gates

Fully Key-Homomorphic Encryption, Arithmetic Circuit ABE, and Compact Garbled Circuits.

ADVANCES IN CRYPTOLOGY - EUROCRYPT 2014, (2014): 533-556

Cited by: 311|Views384
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Abstract

We construct the first (key-policy) attribute-based encryption (ABE) system with short secret keys: the size of keys in our system depends only on the depth of the policy circuit, not its size. Our constructions extend naturally to arithmetic circuits with arbitrary fan-in gates thereby further reducing the circuit depth. Building on this...More

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Introduction
  • This system is key-homomorphic: given a function f : Zq → Zq computed by a poly-size arithmetic circuit, anyone can transform the ciphertext cx into a dual Regev encryption for the public-key matrix
  • This key-homomorphism gives them an ABE for arithmetic circuits: the public parameters contain random matrices B1, .
Highlights
  • We present two new key-policy attribute-based encryption systems
  • Our first system, which is the centerpiece of this paper, is an attribute-based encryption based on the learning with errors problem [Reg05] that supports functions f represented as arithmetic circuits with large fan-in gates
  • We prove selective security from the learning with errors problem (LWE) by using another homomorphic property of the system implemented in an algorithm called Evalsim
  • The encryption algorithm in our system is similar to that in the hierarchicalIBE of Agrawal, Boneh, and Boyen [ABB10]. We show that this system is keyhomomorphic for polynomial-size arithmetic circuits which gives us an attribute-based encryption for such circuits
  • Given the three algorithms (Evalpk, Evalct, Evalsim) for the family of functions F , the Fully Key-Homomorphic PKE system above is selectively secure with respect to F , assuming the (n, q, χ)-Learning with errors assumption holds where n, q, χ are the parameters for the Fully Key-Homomorphic PKE
Results
  • The authors' ABE, when presented with a circuit containing only linear gates, provides a predicate encryption system for inner products in the same security model as [AFV11], but can handle high-weight linear transformations directly, without bit decomposition, thereby obtaining shorter ciphertexts and public-keys.
  • For the authors will assume the existence of three efficient deterministic algorithms Evalpk, Evalct, Evalsim that implement the key-homomorphic features of the scheme and are at the heart of the construction.
  • Given the three algorithms (Evalpk, Evalct, Evalsim) for the family of functions F , the FKHE system above is selectively secure with respect to F , assuming the (n, q, χ)-LWE assumption holds where n, q, χ are the parameters for the FKHE.
  • The authors first describe Eval algorithms for single gates, i.e. when G is the set of functions that each takes k inputs and computes either weighted addition or multiplication:
  • Given FKHE-enabling algorithms (Evalpk, Evalct, Evalsim) for a family of functions F from Section 4.1, the ABE system works as follows:
  • For FKHE-enabling algorithms (Evalpk, Evalct, Evalsim) for a family of functions F the ABE system above is correct and selectively-secure.
  • They observe that the secret key for a function f in an ABE scheme corresponds to the garbled circuit for f , and the ciphertext encrypting an attribute vector x corresponds to the garbled input for x in the reusable garbling scheme.
  • For all polynomials dmax = dmax(λ), there exists a selectively-secure attribute-based encryption with ciphertext size poly for any family of polynomial-size circuits with depth at most dmax and input size , assuming hardness of (d + 1, )−Multilinear Diffie-Hellman Exponent Assumption.
Conclusion
  • – Keygen: The key-generation algorithm takes a circuit C with input bits and a master secret key msk and outputs a secret key skC defined as follows.
  • – Enc: The encryption algorithm takes the master public key mpk, an index x ∈ {0, 1} and a message μ ∈ {0, 1}, and outputs a ciphertext cx defined as follows.
Funding
  • Boneh is supported by NSF, the DARPA PROCEED program, an AFO SR MURI award, a grant from ONR, an IARPA project provided via DoI/NBC, and Google faculty award
  • Gorbunov is supported by Alexander Graham Bell Canada Graduate Scholarship (CGSD3)
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