DGMT: A Fully Dynamic Hash-Based Group Signature

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With the rapid development of quantum technologies, quantum-safe cryptographic schemes have found significant attention. Shor’s quantum algorithms for breaking discrete logarithm (DL) and integer factorization (IF) problems will bring depredation for currently used public key algorithms, including RSA (Rivest–Shamir–Adleman), DH (Diffie-Hellman) key agreement, DSA (Digital Signature Algorithm) and ECC (Elliptic Curve Cryptography), which their security depends on solving mathematical hard problems (IF and DL problem). Therefore, applications and protocols must evolve to be quantum secure in the presence of quantum computers. It is believed that symmetric encryptions and hash functions are resilient to attacks by a quantum adversary. Therefore, signature schemes have been modified so that their security relies on hash functions instead of the aforementioned mathematical hard problems. In this thesis, we consider post-quantum digital group signatures, whose security depends on one-way functions. In practice, these functions are replaced by cryptographic hash functions, which are expected to remain secure in the presence of quantum computers. A group signature is a signature scheme that allows a group member to anonymously sign messages on behalf of the group, while anonymity can be annulled by an opening authority or group manager. In fully dynamic group signature schemes, new members can be added to the group after the initialization phase and existing members can be revoked from the group. The primary aim of this thesis is twofold. Firstly, it aims to conduct a comprehensive analysis of various hash-based group signature schemes, taking into consideration their security models, properties, and limitations. Moreover, this thesis contributes to the development of a novel fully dynamic group signature scheme, named DGMT, which addresses the limitations of previous schemes, and we prove its security (unforgeability, anonymity, and traceability), and provide the complete implementation of the this scheme for the first time. Secondly, the thesis intends to review and evaluate various revocation methods with the objective of identifying potential ways to improve the revocation method utilized in the proposed scheme.
Post Quantum Group signature scheme
Erfanian Azad Soltan, A. (2023). DGMT: a fully dynamic hash-based group signature (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.