On the Impossibility of Basing Identity Based Encryption on Trapdoor Permutations

We ask whether an identity based encryption (IBE) system can be built from simpler public-key primitives. We show that there is no black-box construction of IBE from trapdoor permutations (TDP) or even from chosen ciphertext secure public key encryption (CCA-PKE). These black-box separation results are based on an essential property of IBE, namely that an IBE system is able to compress exponentially many public-keys into a short public parameters string.

[1]  Brent Waters,et al.  Conjunctive, Subset, and Range Queries on Encrypted Data , 2007, TCC.

[2]  Jonathan Katz,et al.  Chosen-Ciphertext Security from Identity-Based Encryption , 2006 .

[3]  Moni Naor,et al.  Nonmalleable Cryptography , 2000, SIAM Rev..

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

[5]  Mihir Bellare,et al.  Random oracles are practical: a paradigm for designing efficient protocols , 1993, CCS '93.

[6]  Yehuda Lindell,et al.  A Simpler Construction of CCA2-Secure Public-Key Encryption under General Assumptions , 2003, EUROCRYPT.

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

[8]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[9]  Anna Lysyanskaya,et al.  Unique Signatures and Verifiable Random Functions from the DH-DDH Separation , 2002, CRYPTO.

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

[11]  Luca Trevisan,et al.  Notions of Reducibility between Cryptographic Primitives , 2004, TCC.

[12]  Daniel R. Simon,et al.  Limits on the efficiency of one-way permutation-based hash functions , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[13]  Luca Trevisan,et al.  Lower bounds on the efficiency of generic cryptographic constructions , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[14]  Elaine Shi,et al.  Multi-Dimensional Range Query over Encrypted Data , 2007, 2007 IEEE Symposium on Security and Privacy (SP '07).

[15]  Brent Waters,et al.  Collusion Resistant Broadcast Encryption with Short Ciphertexts and Private Keys , 2005, CRYPTO.

[16]  Yevgeniy Dodis,et al.  ID-based encryption for complex hierarchies with applications to forward security and broadcast encryption , 2004, CCS '04.

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

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

[19]  Yevgeniy Dodis,et al.  Public Key Broadcast Encryption for Stateless Receivers , 2002, Digital Rights Management Workshop.

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

[21]  Mihir Bellare,et al.  Searchable Encryption Revisited: Consistency Properties, Relation to Anonymous IBE, and Extensions , 2005, Journal of Cryptology.

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

[23]  Steven Myers,et al.  Towards a Separation of Semantic and CCA Security for Public Key Encryption , 2007, TCC.

[24]  Diana K. Smetters,et al.  Secret handshakes from pairing-based key agreements , 2003, 2003 Symposium on Security and Privacy, 2003..

[25]  M. Bellare,et al.  Searchable Encryption Revisited: Consistency Properties, Relation to Anonymous IBE, and Extensions , 2008, Journal of Cryptology.

[26]  Daniel R. Simon,et al.  Finding Collisions on a One-Way Street: Can Secure Hash Functions Be Based on General Assumptions? , 1998, EUROCRYPT.

[27]  Jonathan Katz,et al.  Lower bounds on the efficiency of encryption and digital signature schemes , 2003, STOC '03.

[28]  Sampath Kannan,et al.  The relationship between public key encryption and oblivious transfer , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[29]  Tal Malkin,et al.  On the impossibility of basing trapdoor functions on trapdoor predicates , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

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

[31]  Jonathan Katz,et al.  Chosen-Ciphertext Security from Identity-Based Encryption , 2004, SIAM J. Comput..

[32]  Melissa Chase,et al.  Multi-authority Attribute Based Encryption , 2007, TCC.

[33]  Brent Waters,et al.  Anonymous Hierarchical Identity-Based Encryption (Without Random Oracles) , 2006, CRYPTO.

[34]  Russell Impagliazzo,et al.  Limits on the Provable Consequences of One-way Permutations , 1988, CRYPTO.

[35]  Rafail Ostrovsky,et al.  Public Key Encryption with Keyword Search , 2004, EUROCRYPT.

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

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