Strongly-Optimal Structure Preserving Signatures from Type II Pairings: Synthesis and Lower Bounds

Recent work on structure-preserving signatures studies optimality of these schemes in terms of the number of group elements needed in the verification key and the signature, and the number of pairing-product equations in the verification algorithm. While the size of keys and signatures is crucial for many applications, another important aspect to consider for performance is the time it takes to verify a given signature. By far, the most expensive operation during verification is the computation of pairings. However, the concrete number of pairings that one needs to compute is not captured by the number of pairing-product equations considered in earlier work.

[1]  Ryo Nishimaki,et al.  Tagged One-Time Signatures: Tight Security and Optimal Tag Size , 2013, Public Key Cryptography.

[2]  Kenneth G. Paterson,et al.  Pairings for Cryptographers , 2008, IACR Cryptol. ePrint Arch..

[3]  Alex J. Malozemoff,et al.  Automated Analysis and Synthesis of Block-Cipher Modes of Operation , 2014, 2014 IEEE 27th Computer Security Foundations Symposium.

[4]  Joeri de Ruiter.  Automated algebraic analysis of structure-preserving signature schemes , 2014, IACR Cryptol. ePrint Arch..

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

[6]  Georg Fuchsbauer,et al.  Fair Blind Signatures without Random Oracles , 2010, AFRICACRYPT.

[7]  Jens Groth,et al.  Simulation-Sound NIZK Proofs for a Practical Language and Constant Size Group Signatures , 2006, ASIACRYPT.

[8]  Matthew Green,et al.  Universally Composable Adaptive Oblivious Transfer , 2008, IACR Cryptol. ePrint Arch..

[9]  Richard Zippel,et al.  Probabilistic algorithms for sparse polynomials , 1979, EUROSAM.

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

[11]  Moti Yung,et al.  Group Signatures with Almost-for-Free Revocation , 2012, CRYPTO.

[12]  Jens Groth,et al.  Optimal Structure-Preserving Signatures in Asymmetric Bilinear Groups , 2011, CRYPTO.

[13]  Jan Camenisch,et al.  Oblivious Transfer with Hidden Access Control from Attribute-Based Encryption , 2012, SCN.

[14]  Richard J. Lipton,et al.  A Probabilistic Remark on Algebraic Program Testing , 1978, Inf. Process. Lett..

[15]  Mehdi Tibouchi,et al.  Strongly-optimal structure preserving signatures from Type II pairings: synthesis and lower bounds , 2016, IET Inf. Secur..

[16]  Thomas Peters,et al.  Efficient Completely Context-Hiding Quotable and Linearly Homomorphic Signatures , 2013, Public Key Cryptography.

[17]  Moti Yung,et al.  Group Encryption: Non-interactive Realization in the Standard Model , 2009, ASIACRYPT.

[18]  Gilles Barthe,et al.  Automated Analysis of Cryptographic Assumptions in Generic Group Models , 2014, IACR Cryptol. ePrint Arch..

[19]  Sanjit Chatterjee,et al.  Type 2 Structure-Preserving Signature Schemes Revisited , 2014, ASIACRYPT.

[20]  Benjamin Grégoire,et al.  Fully automated analysis of padding-based encryption in the computational model , 2013, CCS.

[21]  Matthew Green,et al.  Using SMT solvers to automate design tasks for encryption and signature schemes , 2013, CCS.

[22]  Sanjit Chatterjee,et al.  On cryptographic protocols employing asymmetric pairings - The role of Ψ revisited , 2011, Discret. Appl. Math..

[23]  Mehdi Tibouchi,et al.  Unified, Minimal and Selectively Randomizable Structure-Preserving Signatures , 2014, IACR Cryptol. ePrint Arch..

[24]  Jacob T. Schwartz,et al.  Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.

[25]  Georg Fuchsbauer,et al.  Structure-Preserving Signatures and Commitments to Group Elements , 2010, Journal of Cryptology.

[26]  Jens Groth,et al.  Converting Cryptographic Schemes from Symmetric to Asymmetric Bilinear Groups , 2014, CRYPTO.

[27]  Mehdi Tibouchi,et al.  Structure-Preserving Signatures from Type II Pairings , 2014, CRYPTO.

[28]  Ryo Nishimaki,et al.  Constant-Size Structure-Preserving Signatures: Generic Constructions and Simple Assumptions , 2012, Journal of Cryptology.

[29]  Vincent Naessens,et al.  Structure Preserving CCA Secure Encryption and Applications , 2011, ASIACRYPT.

[30]  Jens Groth,et al.  Separating Short Structure-Preserving Signatures from Non-interactive Assumptions , 2011, ASIACRYPT.