Contributions to Group-oriented Anonymous Signatures

<p dir="ltr">Digital signatures play a crucial role in ensuring the authenticity and integrity of information in various applications. While they offer a means to verify the honest sender and guarantee content integrity, there are situations where maintaining the signer’s identity is undesirable. Examples include whistle-blowing or anonymous reporting systems and cryptocurrency transactions where individuals seek to unlink their real identities from their activities.</p><p dir="ltr">To address these privacy concerns, group-oriented anonymous signatures emerge as a significant solution. This variant of digital signatures introduces the property of anonymity, allowing a signer to generate signatures on behalf of a group of members without revealing the actual signer among them. Two prominent types of group-oriented anonymous signatures are group signatures and ring signatures. In group signatures, a group manager forms a group, and any member can produce a signature representing the entire group. On the other hand, ring signatures enable a signer to arbitrarily create a set of users and sign on behalf of them, providing a higher degree of flexibility.</p><p dir="ltr">Despite the extensive body of work related to group signatures and ring signatures, there remain areas that warrant improvement. This thesis focuses on contributing novel and practical constructions to enhance group-oriented anonymous signatures. We briefly outline the advancements made in this thesis below.</p><p dir="ltr">• Firstly, we construct the first quantum-safe unique ring signature, a variant of ring signature, based on lattices. The scheme boasts a logarithmic signature size, providing an efficient and secure solution for post-quantum cryptographic settings.</p><p dir="ltr">• Secondly, we demonstrate a generic construction that converts any existential unforgeability under a chosen message attack (EUF-CMA) signature into a blind-unforgeability (BU) signature. We also design a generic framework transforming any BU signature into a compact post-quantum ring signature. Based on our contribution, anyone can obtain a compact post-quantum ring signature directly from an EUF-CMA signature.</p><p dir="ltr">• Thirdly, we introduce a novel variant of ring signatures called “shrinkable ring signatures” which allows a signer to exclude non-signers from a previously signed signature making the signature represent fewer members. We also introduce a logarithmic-size generic construction and a concrete instantiation based on lattices for SRS.</p><p dir="ltr">• Finally, we propose a fault-tolerant content moderation mechanism for secure messaging systems based on a novel primitive called “Set Pre-constrained Group Signatures with Threshold on Tracing illegal content”. We also construct a generic construction and a pairing-based instantiation for this mechanism.</p><p dir="ltr">These contributions collectively address various aspects of group-oriented anonymous signatures, introducing quantum-safe solutions, short signature size constructions and novel group-oriented anonymous signature variants.</p>