# Techniques: A Unified Framework For Quantum Unforgeability

## What the paper contributes (one paragraph)
The paper builds a single parameterised, game-based security model that unifies the notion of unforgeability against quantum adversaries for both classical primitives (such as MACs and signatures) and quantum primitives (such as quantum money and quantum PUFs). It subsumes the earlier Boneh-Zhandry and blind-unforgeability definitions, captures existential, selective and universal levels, and characterises a "forgery" by mu-distinguishability (fidelity overlap between the challenge and the learning-phase queries) rather than by counting queries. Using this model the authors prove fine-grained possibility and impossibility results: deterministic constructions (HMAC, NMAC and similar) cannot be existentially or selectively unforgeable against general superposition adversaries, shown via a forgery attack built on the Universal Quantum Emulator algorithm. They then give randomised constructions, from a pseudorandom function for classical primitives and a pseudorandom unitary for quantum primitives, that restore selective and universal unforgeability against full quantum adversaries.

## Techniques offered
- **Quantum unforgeability cryptanalysis framework (parameterised game-based security model)** - a unified, parameterised quantum game that an external authentication or signature scheme can be analysed against to certify or refute unforgeability across existential, selective and universal levels and the full spectrum of superposition attacks.
  - guarantee: game-based (reduction) security definition with a hierarchy theorem relating the levels and a proof that prior definitions (blind unforgeability, Boneh-Zhandry) are special instances; mu-distinguishability characterises admissible forgeries.
  - quote: "We develop a general and parameterised quantum game-based security model unifying unforgeability both for classical and quantum constructions allowing us for the first time to present a complete quantum cryptanalysis framework for unforgeability."
- **Universal Quantum Emulator forgery attack** - a cryptanalytic attack that learns the action of a deterministic primitive from input-output samples and forges a valid tag, breaking selective and existential unforgeability of any deterministic classical or quantum construction for any overlap below the orthogonal case.
  - guarantee: constructive impossibility (no-go) result; deterministic MAC constructions such as HMAC and NMAC are shown insecure except in the fully orthogonal challenge case (mu = 1).
  - quote: "To establish our impossibility result, we show an attack based on the Universal Quantum Emulator Algorithm~\cite{marvian2016universal}."
- **Randomised unforgeable construction from a PRF or PRU** - a per-query randomisation scheme that wraps a pseudorandom function (classical primitives) or a pseudorandom unitary (quantum primitives, with an explicit circuit-model randomised oracle) to obtain a selective- and universal-unforgeable primitive secure against general superposition adversaries.
  - guarantee: provable selective unforgeability (qGSU) for all meaningful mu under the PRF, respectively PRU, assumption; relies on an inter-function (pairwise) independence property satisfied by a PRF.
  - quote: "On the other hand, we show that Pseudorandom Functions (PRFs) are sufficient for constructing a quantum selective unforgeable classical primitive against full quantum adversaries (for all reasonable degrees of $\mu$) by proposing a randomised construction."

## Where it could apply
- Target primitive(s): none (no VQE / QAOA / QPE / sampling / Trotterised circuit primitive; the relevant primitives are cryptographic, namely MACs, digital signatures, quantum money and quantum PUFs).
- Target application group(s): crypto_security; platforms_tooling.

## Caveats
This is a quantum-cryptography foundations and cryptanalysis paper. Its central outputs are security definitions, a hierarchy, and possibility/impossibility theorems rather than a runtime capability that plugs into an external quantum-computing vendor or application result. The no-go statements are guarantees attached to the cryptanalysis framework and the emulator attack, not standalone deliverables. The randomised constructions and the framework apply to authentication and unforgeable-primitive design, not to numerical quantum algorithms; no public or paid vendor stack is targeted.