# Quantum-secure message authentication via blind-unforgeability

## TL;DR

This paper introduces a new quantum-aware notion of message unforgeability called blind unforgeability, supporting classical and quantum cryptographic constructions and demonstrating its strength over previous definitions.

## Contribution

The paper proposes the blind unforgeability definition for quantum adversaries, extending classical unforgeability notions and validating it with cryptographic examples and constructions.

## Key findings

- Blind unforgeability coincides with EUF-CMA classically.
- Hash-and-MAC and Lamport signatures are unforgeable under this definition.
- Blind unforgeability is stronger than previous quantum unforgeability notions.

## Abstract

Formulating and designing authentication of classical messages in the presence of adversaries with quantum query access has been a longstanding challenge, as the familiar classical notions of unforgeability do not directly translate into meaningful notions in the quantum setting. A particular difficulty is how to fairly capture the notion of "predicting an unqueried value" when the adversary can query in quantum superposition. We propose a natural definition of unforgeability against quantum adversaries called blind unforgeability. This notion defines a function to be predictable if there exists an adversary who can use "partially blinded" oracle access to predict values in the blinded region. We support the proposal with a number of technical results. We begin by establishing that the notion coincides with EUF-CMA in the classical setting and go on to demonstrate that the notion is satisfied by a number of simple guiding examples, such as random functions and quantum-query-secure pseudorandom functions. We then show the suitability of blind unforgeability for supporting canonical constructions and reductions. We prove that the "hash-and-MAC" paradigm and the Lamport one-time digital signature scheme are indeed unforgeable according to the definition. To support our analysis, we additionally define and study a new variety of quantum-secure hash functions called Bernoulli-preserving. Finally, we demonstrate that blind unforgeability is stronger than a previous definition of Boneh and Zhandry [EUROCRYPT '13, CRYPTO '13] in the sense that we can construct an explicit function family which is forgeable by an attack that is recognized by blind-unforgeability, yet satisfies the definition by Boneh and Zhandry.