ドウシュシャゾウベースノタジュウショメイ，ダイリショメイトタジュウショメイニモトヅクプライベートツイセキプロトコル
Mathieu de Goyon, マチュー デ ゴヨン
The potential development of large-scale quantum computers has raised serious concerns about the security of classical cryptographic systems.In response, the field of post-quantum cryptography has emerged to design cryptographic schemes that remain secure even against quantum adversaries.Isogeny-based cryptography is the most recent addition to post-quantum cryptography and started garnering attention in the 2010s.Digital signature schemes are a fundamental part of public key cryptography, providing authenticity, integrity, and non-repudiation for digital messages.They are essential for secure communication, software updates, electronic transactions, and virtually all systems requiring trust and verification.Although the traditional digital signature scheme consists only of a single prover and verifier, numerous variants have been developed over the years to address specific needs, such as multi-signatures, ring signatures, group signatures, and proxy signatures.These variants extend the functionality of traditional signatures to support more complex security models in real-world applications, such as contact tracing.As isogeny-based cryptography is a relatively young research field, many commonly used cryptographic primitives, such as variants of signature schemes, have not yet been fully developed or widely implemented.This leaves room for exploration and optimization in designing secure and efficient isogeny-based alternatives, while taking advantage of its strength with its small keys and signature compared to other post-quantum based constructions such as lattice.Multi-signature schemes have been extensively studied for decades and form a well-established area of research in cryptography.These schemes enable a group of users to collaboratively generate a single, compact signature on a shared message, ensuring that all designated parties have approved the content.Their efficiency and security properties make them particularly valuable in applications such as blockchain transactions and distributed systems.Active security in multi-signature schemes requires the signature to be unforgeable even in the worst-case scenario, where malicious signers would collude to generate a multi-signature in a group with a single honest signer.Our first contribution is to propose an actively secure isogeny-based multi-signature scheme.Proxy signature schemes have been the subject of extensive research over the years, offering cryptographic solutions for secure delegation of signing authority.These schemes allows an original signer to designate a proxy signer to generate signatures on their behalf, within the limitations imposed by the original signer.Such mechanisms are particularly useful in settings like secure communications, delegated access control, and corporate approval systems where it is essential for operations to continue even in the absence of the designated signer.Proxy I would like to express my deepest gratitude to everyone who has supported me throughout my Ph.D. journey.First and foremost, I am deeply grateful to my supervisor, Professor Atsuko Miyaji, for giving me a chance to experience the field of research as an exchange student before accepting me once again as a Ph.D student.Her invaluable support and guidance throughout the course of those 3 years as a Ph.D student enabled me to make it this far.Additionally, I am deeply grateful to the NEC Corporation for its C&C Fellowship, as well as the Jisedai Program.Their generous support eased my financial burdens, allowing to focus completely on my research.I am also deeply grateful to the professors, staff, and colleagues at Miyaji Lab, who were always there whenever I needed it.I want to especially thank Hide Miyaji, for welcoming me with open arms as soon as I arrived for the first time in Japan and supporting me throughout my Ph.D journey.I am also profoundly grateful to Mohamed Bourefis, my French comrade, who shares a very similar
•Jan 1, 2026•0 citations