Access Control Encryption Based on LWE

Damgard et al. proposed a new primitive called access control encryption (ACE) [6] which not only protects the privacy of the message, but also controls the ability of the sender to send the message. We will give a new construction based on the Learning with Error (LWE) assumption [12], which is one of the two open problems in [6]. Although there are many public key encryption schemes based on LWE and supporting homomorphic operations. We find that not every scheme can be used to build ACE. In order to keep the security and correctness of ACE, the random constant chosen by the sanitizer should satisfy stricter condition. We also give a different security proof of ACE based on LWE from it based on DDH. We will see that although the modulus of LWE should be super-polynomial, the ACE scheme is still as secure as the general public key encryption scheme based on the lattice [5].

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

[2]  Vinod Vaikuntanathan,et al.  Efficient Fully Homomorphic Encryption from (Standard) LWE , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[3]  Vinod Vaikuntanathan,et al.  Lattice-based FHE as secure as PKE , 2014, IACR Cryptol. ePrint Arch..

[4]  References , 1971 .

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

[6]  Chris Peikert,et al.  On Ideal Lattices and Learning with Errors over Rings , 2010, JACM.

[7]  Georg Fuchsbauer,et al.  Access Control Encryption for Equality, Comparison, and More , 2017, IACR Cryptol. ePrint Arch..

[8]  Ivan Damgård,et al.  Access Control Encryption: Enforcing Information Flow with Cryptography , 2016, TCC.

[9]  Craig Gentry,et al.  (Leveled) fully homomorphic encryption without bootstrapping , 2012, ITCS '12.

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

[11]  GentryCraig,et al.  Leveled) Fully Homomorphic Encryption without Bootstrapping , 2014 .

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

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

[14]  Zvika Brakerski,et al.  Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP , 2012, CRYPTO.