Compact Inner Product Encryption from LWE

Predicate encryption provides fine-grained access control and has attractive applications. In this paper, We construct an compact inner product encryption scheme from the standard Learning with Errors (LWE) assumption that has compact public-key and achieves weakly attribute-hiding in the standard model. In particular, our scheme only needs two public matrices to support inner product over vector space \(\mathbb {Z}_q^{\log \lambda }\), and \((\lambda / \log \lambda )\) public matrices to support vector space \(\mathbb {Z}_q^{\lambda }\).

[1]  Dan Boneh,et al.  Efficient Lattice (H)IBE in the Standard Model , 2010, EUROCRYPT.

[2]  Brent Waters,et al.  Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based , 2013, CRYPTO.

[3]  Matthew K. Franklin,et al.  Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.

[4]  Brent Waters,et al.  Attribute-based encryption for fine-grained access control of encrypted data , 2006, CCS '06.

[5]  Brent Waters,et al.  Functional Encryption: Definitions and Challenges , 2011, TCC.

[6]  Craig Gentry,et al.  Trapdoors for hard lattices and new cryptographic constructions , 2008, IACR Cryptol. ePrint Arch..

[7]  David Cash,et al.  Bonsai Trees, or How to Delegate a Lattice Basis , 2010, Journal of Cryptology.

[8]  Jonathan Katz,et al.  Predicate Encryption Supporting Disjunctions, Polynomial Equations, and Inner Products , 2008, Journal of Cryptology.

[9]  Adam O'Neill,et al.  Definitional Issues in Functional Encryption , 2010, IACR Cryptol. ePrint Arch..

[10]  Chris Peikert,et al.  Generating Shorter Bases for Hard Random Lattices , 2009, Theory of Computing Systems.

[11]  Adi Shamir,et al.  Identity-Based Cryptosystems and Signature Schemes , 1984, CRYPTO.

[12]  Vinod Vaikuntanathan,et al.  Attribute-based encryption for circuits , 2013, STOC '13.

[13]  Craig Gentry,et al.  Fully Key-Homomorphic Encryption, Arithmetic Circuit ABE and Compact Garbled Circuits , 2014, EUROCRYPT.

[14]  Craig Gentry,et al.  Fully homomorphic encryption using ideal lattices , 2009, STOC '09.

[15]  Vinod Vaikuntanathan,et al.  Functional Encryption for Inner Product Predicates from Learning with Errors , 2011, IACR Cryptol. ePrint Arch..

[16]  Chris Peikert,et al.  Faster Bootstrapping with Polynomial Error , 2014, CRYPTO.

[17]  Keita Xagawa,et al.  Improved (Hierarchical) Inner-Product Encryption from Lattices , 2013, Public Key Cryptography.

[18]  Feng-Hao Liu,et al.  Vector Encoding over Lattices and Its Applications , 2017, IACR Cryptol. ePrint Arch..

[19]  Chris Peikert,et al.  Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller , 2012, IACR Cryptol. ePrint Arch..

[20]  Suela Kodra.  Fuzzy extractors : How to generate strong keys from biometrics and other noisy data , 2015 .

[21]  Henri Gilbert,et al.  Advances in Cryptology - EUROCRYPT 2010, 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Monaco / French Riviera, May 30 - June 3, 2010. Proceedings , 2010, EUROCRYPT.

[22]  Miklós Ajtai,et al.  Generating hard instances of lattice problems (extended abstract) , 1996, STOC '96.

[23]  Shweta Agrawal,et al.  Stronger Security for Reusable Garbled Circuits, General Definitions and Attacks , 2017, CRYPTO.

[24]  Brent Waters,et al.  Conjunctive, Subset, and Range Queries on Encrypted Data , 2007, TCC.

[25]  Brent Waters,et al.  Ciphertext-Policy Attribute-Based Encryption , 2007, 2007 IEEE Symposium on Security and Privacy (SP '07).

[26]  Oded Regev,et al.  On lattices, learning with errors, random linear codes, and cryptography , 2005, STOC '05.