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Post-Quantum Secure Group Signatures

Laurens Porzenheim

Published Jan 1, 2019• 0 citations
OpenAlex

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This paper presents a robust lattice-based digital signature scheme that leverages matrix groups to enhance post-quantum security. Built on the hardness of lattice problems such as the Shortest Vector Problem (SVP) and Learning With Errors (LWE), combined with the complexity of the Matrix Group Conjugacy Problem our scheme demonstrates both theoretical and practical security. We rigorously establish the (MGCP), mathematical foundations, analyze the computational complexity, and provide numerical simulations to evaluate performance. This approach contributes a unique blend of lattice and matrix group theory, offering new insights and possibilities in post-quantum cryptography.

Asian journal of mathematics and computer research•Nov 27, 2024•1 citation
Group signatures are an important cryptographic primitive providing both anonymity and accountability to signatures. Accountable ring signatures (ARS) combine features from ring signatures (RS) and group signatures (GS), and can be directly transformed into either of both. While there exist extensive works on constructing GS from various post-quantum assumptions, there has not been any research using isogeny-based assumptions. In this work, we propose the first isogeny-based GS, which is a direct result of our isogeny-based ARS. Our schemes are based on the decisional CSIDH assumption (D-CSIDH) and are proven secure under the quantum random oracle model (QROM). This work is also the first post-quantum ARS and GS that are proven QROM-secure.
This paper presents a robust lattice-based digital signature scheme that leverages matrix groups to enhance post-quantum security. Built on the hardness of lattice problems such as the Shortest Vector Problem (SVP) and Learning With Errors (LWE), combined with the complexity of the Matrix Group Conjugacy Problem our scheme demonstrates both theoretical and practical security. We rigorously establish the (MGCP), mathematical foundations, analyze the computational complexity, and provide numerical simulations to evaluate performance. This approach contributes a unique blend of lattice and matrix group theory, offering new insights and possibilities in post-quantum cryptography.