New Security Proof for the Boneh-Boyen IBE: Tight Reduction in Unbounded Multi-challenge Security

Identity-based encryption IBE is an advanced form of public key encryption and one of the most important cryptographic primitives. Of the many constructions of IBE schemes, the one proposed by Boneh and Boyen in Eurocrypt 2004 is quite important from both practical and theoretical points of view. The scheme was standardized as IEEE P1363.3 and is the basis for many subsequent constructions. In this paper, we investigate its multi-challenge security, which means that an adversary is allowed to query challenge ciphertexts multiple times rather than only once. Since single-challenge security implies multi-challenge security, and since Boneh and Boyen provided a security proof for the scheme in the single-challenge setting, the scheme is also secure in the multi-challenge setting. However, this reduction results in a large security loss. Instead, we give tight security reduction for the scheme in the multi-challenge setting. Our reduction is tight even if the number of challenge queries is not fixed in advance that is, the queries are unbounded. Unfortunately, we are only able to prove the security in a selective setting and rely on a non-standard parameterized assumption. Nevertheless, we believe that our new security proof is of interest and provides new insight into the security of the Boneh-Boyen IBE scheme.

[1]  Craig Gentry,et al.  Space-Efficient Identity Based EncryptionWithout Pairings , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[2]  Goichiro Hanaoka,et al.  A Framework and Compact Constructions for Non-monotonic Attribute-Based Encryption , 2014, Public Key Cryptography.

[3]  Ran Canetti,et al.  A Forward-Secure Public-Key Encryption Scheme , 2003, Journal of Cryptology.

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

[5]  Ran Canetti,et al.  The random oracle methodology, revisited , 2000, JACM.

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

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

[8]  Jacob C. N. Schuldt,et al.  On the Impossibility of Constructing Efficient Key Encapsulation and Programmable Hash Functions in Prime Order Groups , 2012, CRYPTO.

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

[10]  Brent Waters,et al.  New Constructions and Proof Methods for Large Universe Attribute-Based Encryption , 2012, IACR Cryptol. ePrint Arch..

[11]  Sanjit Chatterjee,et al.  Generalization of the Selective-ID Security Model for HIBE Protocols , 2006, Public Key Cryptography.

[12]  Moni Naor,et al.  Number-theoretic constructions of efficient pseudo-random functions , 2004, JACM.

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

[14]  David Cash,et al.  Bonsai Trees, or How to Delegate a Lattice Basis , 2010, EUROCRYPT.

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

[16]  Mihir Bellare,et al.  A concrete security treatment of symmetric encryption , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[17]  David Galindo,et al.  The Exact Security of Pairing Based Encryption and Signature Schemes , 2004 .

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

[19]  Ben Lynn,et al.  Toward Hierarchical Identity-Based Encryption , 2002, EUROCRYPT.

[20]  Tibor Jager,et al.  Short Signatures From Weaker Assumptions , 2011, IACR Cryptol. ePrint Arch..

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

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

[23]  Jung Hee Cheon,et al.  Security Analysis of the Strong Diffie-Hellman Problem , 2006, EUROCRYPT.

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

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

[26]  Allison Bishop,et al.  Revocation Systems with Very Small Private Keys , 2010, 2010 IEEE Symposium on Security and Privacy.

[27]  Brent Waters,et al.  Ciphertext-Policy Attribute-Based Encryption: An Expressive, Efficient, and Provably Secure Realization , 2011, Public Key Cryptography.

[28]  Brent Waters,et al.  Functional Encryption for Regular Languages , 2012, CRYPTO.

[29]  Nuttapong Attrapadung,et al.  Dual System Encryption via Doubly Selective Security: Framework, Fully-secure Functional Encryption for Regular Languages, and More , 2014, IACR Cryptol. ePrint Arch..

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

[31]  Brent Waters,et al.  Practical constructions and new proof methods for large universe attribute-based encryption , 2013, CCS.

[32]  Allison Bishop,et al.  New Techniques for Dual System Encryption and Fully Secure HIBE with Short Ciphertexts , 2010, IACR Cryptol. ePrint Arch..

[33]  Hideki Imai,et al.  Efficient Identity-Based Encryption with Tight Security Reduction , 2007, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[34]  Craig Gentry,et al.  Hierarchical ID-Based Cryptography , 2002, ASIACRYPT.

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

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

[37]  Rafail Ostrovsky,et al.  Lossy Encryption: Constructions from General Assumptions and Efficient Selective Opening Chosen Ciphertext Security , 2011, ASIACRYPT.

[38]  Dan Boneh,et al.  Short Signatures Without Random Oracles , 2004, EUROCRYPT.

[39]  Kenneth G. Paterson,et al.  Programmable Hash Functions in the Multilinear Setting , 2013, CRYPTO.

[40]  Xavier Boyen,et al.  Lattice Mixing and Vanishing Trapdoors A Framework for Fully Secure Short Signatures and more , 2010 .

[41]  Craig Gentry,et al.  Hierarchical Identity Based Encryption with Polynomially Many Levels , 2009, TCC.

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