On New Zero-Knowledge Proofs for Lattice-Based Group Signatures with Verifier-Local Revocation

For lattice-based group signatures with verifier-local revocation (VLR), a group member who issues a signature on behalf of the whole group can validly prove to the verifiers with an efficient non-interactive zero-knowledge proof protocol, from which the verifiers only come to the conclusion that the signer is a certified group member who owns a valid secret signing key and its corresponding revocation token is out of the revocation list. The first such construction was introduced by Langlois et al. (PKC 2014), furthermore, a full and corrected version was proposed in TCS 2018. However, both schemes are within the structure of Bonsai Trees, and thus the bit-sizes of the group public-key and the group member secret-key are proportional to \(\log N\), where N is the maximum number of group members, therefore both constructions are not suitable for a large group.

[1]  Huaxiong Wang,et al.  Group Signatures from Lattices: Simpler, Tighter, Shorter, Ring-Based , 2015, Public Key Cryptography.

[2]  Takeshi Koshiba,et al.  Achieving Strong Security and Verifier-Local Revocation for Dynamic Group Signatures from Lattice Assumptions , 2018, STM.

[3]  Huaxiong Wang,et al.  Forward-Secure Group Signatures from Lattices , 2018, PQCrypto.

[4]  Mihir Bellare,et al.  Foundations of Group Signatures: Formal Definitions, Simplified Requirements, and a Construction Based on General Assumptions , 2003, EUROCRYPT.

[5]  Huaxiong Wang,et al.  Zero-Knowledge Arguments for Lattice-Based Accumulators: Logarithmic-Size Ring Signatures and Group Signatures Without Trapdoors , 2016, Journal of Cryptology.

[6]  Huaxiong Wang,et al.  Lattice-based Group Signature Scheme with Verifier-local Revocation , 2014, IACR Cryptol. ePrint Arch..

[7]  Oded Regev,et al.  On lattices, learning with errors, random linear codes, and cryptography , 2005, STOC '05.

[8]  Chris Peikert,et al.  Hardness of SIS and LWE with Small Parameters , 2013, CRYPTO.

[9]  Mihir Bellare,et al.  Foundations of Group Signatures: The Case of Dynamic Groups , 2005, CT-RSA.

[10]  Zhenfeng Zhang,et al.  Simpler Efficient Group Signatures from Lattices , 2015, Public Key Cryptography.

[11]  Yupu Hu,et al.  Lattice-based group signature with verifier-local revocation , 2017 .

[12]  Huaxiong Wang,et al.  Signature Schemes with Efficient Protocols and Dynamic Group Signatures from Lattice Assumptions , 2016, ASIACRYPT.

[13]  Aggelos Kiayias,et al.  Secure scalable group signature with dynamic joins and separable authorities , 2006, Int. J. Secur. Networks.

[14]  Huaxiong Wang,et al.  Constant-Size Group Signatures from Lattices , 2018, Public Key Cryptography.

[15]  Damien Stehlé,et al.  Lattice-Based Group Signatures with Logarithmic Signature Size , 2013, ASIACRYPT.

[16]  Keisuke Tanaka,et al.  Concurrently Secure Identification Schemes Based on the Worst-Case Hardness of Lattice Problems , 2008, ASIACRYPT.

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

[18]  Benoît Libert,et al.  A Lattice-Based Group Signature Scheme with Message-Dependent Opening , 2016, ACNS.

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

[20]  Takeshi Koshiba,et al.  Zero-Knowledge Proof for Lattice-Based Group Signature Schemes with Verifier-Local Revocation , 2018, NBiS.

[21]  Jens Groth,et al.  Foundations of Fully Dynamic Group Signatures , 2016, Journal of Cryptology.

[22]  Huaxiong Wang,et al.  Lattice-Based Group Signatures: Achieving Full Dynamicity with Ease , 2017, ACNS.

[23]  Jan Camenisch,et al.  Fully Anonymous Attribute Tokens from Lattices , 2012, SCN.

[24]  Hovav Shacham,et al.  Group signatures with verifier-local revocation , 2004, CCS '04.

[25]  Damien Stehlé,et al.  Improved Zero-Knowledge Proofs of Knowledge for the ISIS Problem, and Applications , 2013, Public Key Cryptography.

[26]  Jonathan Katz,et al.  A Group Signature Scheme from Lattice Assumptions , 2010, IACR Cryptol. ePrint Arch..

[27]  Yanhua Zhang,et al.  Simpler Efficient Group Signature Scheme with Verifier-Local Revocation from Lattices , 2016, KSII Trans. Internet Inf. Syst..