Witness Encryption from Instance Independent Assumptions

Witness encryption was proposed by Garg, Gentry, Sahai, and Waters as a means to encrypt to an instance, x, of an NP language and produce a ciphertext. In such a system, any decryptor that knows of a witness w that x is in the language can decrypt the ciphertext and learn the message. In addition to proposing the concept, their work provided a candidate for a witness encryption scheme built using multilinear encodings. However, one significant limitation of the work is that the candidate had no proof of security (other than essentially assuming the scheme secure).

[1]  Allison Bishop,et al.  Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting , 2012, EUROCRYPT.

[2]  Martin Tompa,et al.  Random self-reducibility and zero knowledge interactive proofs of possession of information , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[3]  Rafail Ostrovsky,et al.  Resettable Statistical Zero Knowledge , 2012, IACR Cryptol. ePrint Arch..

[4]  Rafael Pass,et al.  Indistinguishability Obfuscation from Semantically-Secure Multilinear Encodings , 2014, CRYPTO.

[5]  Mihir Bellare,et al.  Adaptive Witness Encryption and Asymmetric Password-Based Cryptography , 2015, Public Key Cryptography.

[6]  Brent Waters,et al.  Witness encryption and its applications , 2013, STOC '13.

[7]  Brent Waters,et al.  Candidate Indistinguishability Obfuscation and Functional Encryption for all Circuits , 2013, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.

[8]  Nathan Linial,et al.  Collective coin flipping, robust voting schemes and minima of Banzhaf values , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[9]  Allison Bishop,et al.  New Proof Methods for Attribute-Based Encryption: Achieving Full Security through Selective Techniques , 2012, CRYPTO.

[10]  Clifford C. Cocks.  An Identity Based Encryption Scheme Based on Quadratic Residues , 2001, IMACC.

[11]  Brent Waters,et al.  Fully Collusion Resistant Traitor Tracing with Short Ciphertexts and Private Keys , 2006, EUROCRYPT.

[12]  Brent Waters,et al.  Fuzzy Identity-Based Encryption , 2005, EUROCRYPT.

[13]  Amos Fiat,et al.  Tracing Traitors , 1994, CRYPTO.

[14]  Brent Waters,et al.  A fully collusion resistant broadcast, trace, and revoke system , 2006, CCS '06.

[15]  Jung Hee Cheon,et al.  Beyond the Limitation of Prime-Order Bilinear Groups, and Round Optimal Blind Signatures , 2012, TCC.

[16]  Vinod Vaikuntanathan,et al.  Predicate Encryption for Circuits from LWE , 2015, CRYPTO.

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

[18]  Craig Gentry,et al.  Candidate Multilinear Maps from Ideal Lattices , 2013, EUROCRYPT.

[19]  Yael Tauman Kalai,et al.  On the impossibility of obfuscation with auxiliary input , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[20]  Allison Lewko,et al.  Tools for simulating features of composite order bilinear groups in the prime order setting , 2012 .

[21]  David Mandell Freeman,et al.  Converting Pairing-Based Cryptosystems from Composite-Order Groups to Prime-Order Groups , 2010, EUROCRYPT.

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

[23]  Tatsuaki Okamoto,et al.  Fully Secure Functional Encryption with General Relations from the Decisional Linear Assumption , 2010, IACR Cryptol. ePrint Arch..

[24]  Allison Bishop,et al.  Fully Secure Functional Encryption: Attribute-Based Encryption and (Hierarchical) Inner Product Encryption , 2010, EUROCRYPT.

[25]  Yael Tauman Kalai,et al.  How to Run Turing Machines on Encrypted Data , 2013, CRYPTO.

[26]  Jean-Sébastien Coron,et al.  Practical Multilinear Maps over the Integers , 2013, CRYPTO.

[27]  Amos Fiat,et al.  Broadcast Encryption , 1993, CRYPTO.

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

[29]  Dan Boneh,et al.  Applications of Multilinear Forms to Cryptography , 2002, IACR Cryptol. ePrint Arch..

[30]  Brent Waters,et al.  Attribute-Based Encryption for Circuits from Multilinear Maps , 2012, CRYPTO.