Securité de l'hypothèse One-More Discrete-Logarithm et des signatures de Schnorr aveugles.
Antoine Plouviez · HAL (Le Centre pour la Communication Scientifique Directe) · 2021
The one more-discrete logarithm assumption (OMDL) is central to the security analysis of identification protocols, blind signatures and multi-signature schemes, most notably blind Schnorr signatures and the recent MuSig2 multi-signatures. Despite its wide use, surprisingly, OMDL is lacking any rigorous analysis. In this work we give rigorous proofs in the Generic Group Model of OMDL and a related assumption. The Schnorr blind signing protocol allows blind issuing of Schnorr signatures, one of the most widely used signatures. As for OMDL, despite its practical relevance, its security analysis (based on OMDL) is unsatisfactory. We analyze the security of these schemes in the algebraic group model (AGM), an idealized model closer to the standard model than the GGM.