Blind Unforgeability implies Plus-One Unforgeability

2026-09-30

AI Summary

This study addresses the open problem in quantum cryptography concerning the implication relationship between quantum blind unforgeability and one-more unforgeability. To resolve this, we propose a smoothing technique termed "coherent reweighted query history," which enables efficient adversary transformation within the frameworks of quantum query algorithms and black-box models. We rigorously prove that quantum blind unforgeability implies one-more unforgeability, establishing the former as a strictly stronger security notion. Notably, this reduction incurs only an inverse-polynomial security loss. Consequently, our work resolves a long-standing open problem in the literature and provides essential theoretical foundations for the security analysis of quantum cryptographic protocols.

Abstract

We prove that quantum blind-unforgeability implies quantum plus-one unforgeability, settling an open question in the literature. Since plus-one unforgeability is known not to imply blind-unforgeability, our result establishes that blind-unforgeability is \emph{strictly stronger} than plus-one unforgeability in the quantum setting. The implication is proven using a new \emph{smoothing} technique that coherently rescales the query histories of a quantum-query algorithm in a black-box manner. This enables us to transform any successful plus-one attacker into a blind-unforgeability attacker with only inverse-polynomial loss. Our proof represents a conceptual shift from merely extracting a useful query history as in earlier attempts, which we show inevitably fails in general, to first coherently reshaping how query histories interfere.

Problem

• Blind Unforgeability
• Plus-One Unforgeability
• Quantum Security
• Quantum Cryptography

Innovation

• Blind Unforgeability
• Plus-One Unforgeability
• Smoothing Technique
• Quantum Query Algorithm
• Coherent Rescaling