Tools for simulating features of composite order bilinear groups in the prime order setting

In this paper, we explore a general methodology for converting composite order pairing-based cryptosystems into the prime order setting. We employ the dual pairing vector space approach initiated by Okamoto and Takashima and formulate versatile tools in this framework that can be used to translate composite order schemes for which the prior techniques of Freeman were insufficient. Our techniques are typically applicable for composite order schemes relying on the canceling property and proven secure from variants of the subgroup decision assumption, and will result in prime order schemes that are proven secure from the decisional linear assumption. As an instructive example, we obtain a translation of the Lewko-Waters composite order IBE scheme. This provides a close analog of the Boneh-Boyen IBE scheme that is proven fully secure from the decisional linear assumption. In the full version of this paper, we also provide a translation of the Lewko-Waters unbounded HIBE scheme.

[1]  Allison Bishop,et al.  Achieving Leakage Resilience through Dual System Encryption , 2011, TCC.

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

[3]  Rafail Ostrovsky,et al.  Perfect Non-Interactive Zero Knowledge for NP , 2006, IACR Cryptol. ePrint Arch..

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

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

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

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

[8]  Brent Waters,et al.  Building efficient fully collusion-resilient traitor tracing and revocation schemes , 2010, CCS '10.

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

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

[11]  Tatsuaki Okamoto,et al.  Homomorphic Encryption and Signatures from Vector Decomposition , 2008, Pairing.

[12]  Allison Bishop,et al.  Unbounded HIBE and Attribute-Based Encryption , 2011, IACR Cryptol. ePrint Arch..

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

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

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

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

[17]  Brent Waters,et al.  Identity-Based Encryption Secure against Selective Opening Attack , 2011, TCC.

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

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

[20]  Dan Boneh,et al.  Hierarchical Identity Based Encryption with Constant Size Ciphertext , 2005, EUROCRYPT.

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

[22]  Elaine Shi,et al.  Delegating Capabilities in Predicate Encryption Systems , 2008, ICALP.

[23]  Allison Bishop,et al.  Decentralizing Attribute-Based Encryption , 2011, IACR Cryptol. ePrint Arch..

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

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

[26]  Rafail Ostrovsky,et al.  Non-interactive Zaps and New Techniques for NIZK , 2006, CRYPTO.

[27]  Rafail Ostrovsky,et al.  Attribute-based encryption with non-monotonic access structures , 2007, CCS '07.

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

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

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

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

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

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

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

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

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

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

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

[39]  Hovav Shacham,et al.  Limitations on Transformations from Composite-Order to Prime-Order Groups: The Case of Round-Optimal Blind Signatures , 2010, ASIACRYPT.