Switching Lemma for Bilinear Tests and Constant-Size NIZK Proofs for Linear Subspaces

We state a switching lemma for tests on adversarial responses involving bilinear pairings in hard groups, where the tester can effectively switch the randomness used in the test from being given to the adversary at the outset to being chosen after the adversary commits its response. The switching lemma can be based on any k-linear hardness assumptions on one of the groups. In particular, this enables convenient information theoretic arguments in the construction of sequence of games proving security of cryptographic schemes, mimicking proofs and constructions in the random oracle model.

[1]  Rafail Ostrovsky,et al.  Circular-Secure Encryption from Decision Diffie-Hellman , 2008, CRYPTO.

[2]  Ronald Cramer,et al.  A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack , 1998, CRYPTO.

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

[4]  I. Damgård,et al.  The protocols. , 1989, The New Zealand nursing journal. Kai tiaki.

[5]  Georg Fuchsbauer,et al.  Batch Groth-Sahai , 2010, ACNS.

[6]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[7]  Eike Kiltz,et al.  Secure Hybrid Encryption from Weakened Key Encapsulation , 2007, CRYPTO.

[8]  Jan Camenisch,et al.  A public key encryption scheme secure against key dependent chosen plaintext and adaptive chosen ciphertext attacks , 2009, IACR Cryptol. ePrint Arch..

[9]  Amit Sahai,et al.  Efficient Non-interactive Proof Systems for Bilinear Groups , 2008, EUROCRYPT.

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

[11]  Amos Fiat,et al.  How to Prove Yourself: Practical Solutions to Identification and Signature Problems , 1986, CRYPTO.

[12]  Moti Yung,et al.  Non-Malleability from Malleability: Simulation-Sound Quasi-Adaptive NIZK Proofs and CCA2-Secure Encryption from Homomorphic Signatures , 2014, IACR Cryptol. ePrint Arch..

[13]  Eike Kiltz,et al.  Quasi-Adaptive NIZK for Linear Subspaces Revisited , 2015, IACR Cryptol. ePrint Arch..

[14]  Carla Ràfols,et al.  QA-NIZK Arguments in Asymmetric Groups: New Tools and New Constructions , 2015, ASIACRYPT.

[15]  Mihir Bellare,et al.  Relations among Notions of Security for Public-Key Encryption Schemes , 1998, IACR Cryptol. ePrint Arch..

[16]  Hovav Shacham,et al.  Short Group Signatures , 2004, CRYPTO.

[17]  D. Eisenbud.  Commutative Algebra: with a View Toward Algebraic Geometry , 1995 .

[18]  David Pointcheval,et al.  Disjunctions for Hash Proof Systems: New Constructions and Applications , 2015, EUROCRYPT.

[19]  Moti Yung,et al.  Compactly Hiding Linear Spans - Tightly Secure Constant-Size Simulation-Sound QA-NIZK Proofs and Applications , 2015, ASIACRYPT.

[20]  Charanjit S. Jutla,et al.  Dual-System Simulation-Soundness with Applications to UC-PAKE and More , 2015, ASIACRYPT.

[21]  Hovav Shacham,et al.  A Cramer-Shoup Encryption Scheme from the Linear Assumption and from Progressively Weaker Linear Variants , 2007, IACR Cryptol. ePrint Arch..