Fully, (Almost) Tightly Secure IBE from Standard Assumptions

We present the first fully secure Identity-Based Encryption scheme (IBE) from the standard assumptions where the security loss depends only on the security parameter and is independent of the number of secret key queries. This partially answers an open problem posed by Waters (Eurocrypt 2005). Our construction combines Waters’ dual system encryption methodology (Crypto 2009) with the Naor-Reingold pseudo-random function (J. ACM, 2004) in a novel way. The security of our scheme relies on the DLIN assumption in prime-order groups.

[1]  Dan Boneh,et al.  Lattice Basis Delegation in Fixed Dimension and Shorter-Ciphertext Hierarchical IBE , 2010, CRYPTO.

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

[3]  Tibor Jager,et al.  Waters Signatures with Optimal Security Reduction , 2012, Public Key Cryptography.

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

[5]  Craig Gentry,et al.  Practical Identity-Based Encryption Without Random Oracles , 2006, EUROCRYPT.

[6]  Dan Boneh,et al.  Evaluating 2-DNF Formulas on Ciphertexts , 2005, TCC.

[7]  Hoeteck Wee,et al.  Dual System Groups and its Applications - Compact HIBE and More , 2014, IACR Cryptol. ePrint Arch..

[8]  Hoeteck Wee,et al.  Dual System Encryption via Predicate Encodings , 2014, TCC.

[9]  Mihir Bellare,et al.  Simulation without the Artificial Abort: Simplified Proof and Improved Concrete Security for Waters' IBE Scheme , 2009, EUROCRYPT.

[10]  Dan Boneh,et al.  Efficient Selective-ID Secure Identity Based Encryption Without Random Oracles , 2004, IACR Cryptol. ePrint Arch..

[11]  Tibouchi Mehdi,et al.  Tightly-Secure Signatures From Lossy Identification Schemes , 2012 .

[12]  A. Lewko,et al.  Fully Secure HIBE with Short Ciphertexts , 2009 .

[13]  Allison Bishop,et al.  Efficient pseudorandom functions from the decisional linear assumption and weaker variants , 2009, CCS.

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

[15]  Brent Waters,et al.  Efficient Identity-Based Encryption Without Random Oracles , 2005, EUROCRYPT.

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

[17]  Brent Waters,et al.  Dual System Encryption: Realizing Fully Secure IBE and HIBE under Simple Assumptions , 2009, IACR Cryptol. ePrint Arch..

[18]  Moni Naor,et al.  Number-theoretic constructions of efficient pseudo-random functions , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

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

[20]  Saqib A. Kakvi,et al.  Optimal security proofs for full domain hash, revisited , 2012 .

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

[22]  Jonathan Katz,et al.  A Forward-Secure Public-Key Encryption Scheme , 2003, Journal of Cryptology.

[23]  Tibor Jager,et al.  Tightly secure signatures and public-key encryption , 2012, Designs, Codes and Cryptography.

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

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

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

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

[28]  Dan Boneh,et al.  Secure Identity Based Encryption Without Random Oracles , 2004, CRYPTO.

[29]  Hoeteck Wee,et al.  Fully, (Almost) Tightly Secure IBE and Dual System Groups , 2013, CRYPTO.

[30]  Tatsuaki Okamoto,et al.  Hierarchical Predicate Encryption for Inner-Products , 2009, ASIACRYPT.