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Quantum

A quantum algorithm for one-shot signatures

Gopikrishnan Muraleedharan, Minh Thuy Truc Pham, Vir Pathak, Thomas Gardner, Chuanqi Zhang, Gavin K. Brennen

Featured June 24, 2026

Original Paper

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Simply

This paper shows how to build a quantum one-shot signature where a secret key, stored as a quantum state, can only be used once before it disappears, making it impossible to copy or reuse.

In depth
The paper provides the first circuit-level implementation of one-shot signatures (OSS), a quantum cryptographic primitive where a secret key is a quantum state that self-destructs after one use. The authors introduce a novel key generation method that leverages Bruhat decomposition to efficiently create a uniform superposition over a hidden affine coset. Furthermore, they propose a streamlined multi-bit signing procedure that uses a global measurement and a single quantum translation, significantly reducing circuit depth compared to prior iterative approaches.

Key Takeaways

  • 1
    The paper delivers the first explicit quantum circuit implementation for one-shot signatures, translating theoretical protocols into concrete algorithms for key generation, signing, and verification.
  • 2
    A novel key generation method is introduced, combining a GGM-based puncturable pseudorandom function (PPRF) with Bruhat decomposition to efficiently sample random affine cosets.
  • 3
    The authors propose a global measurement and translation approach for multi-bit signing, which simplifies the quantum circuit and reduces depth compared to iterative bit-flipping methods.

Conceptual Flow

HIGH LEVEL
1
Methodology: How Quantum One-Shot Signatures Work

The system creates a special quantum secret key that can only be used once to sign a message, and then it vanishes, while a public key lets anyone check the signature.

Secret Key (Quantum)
Message (Classical)
Sign Once
Signature (Classical)
Secret Key (Gone)
2
Results: Efficient Circuit Implementation

The paper makes these quantum signatures practical by designing clever quantum circuits that generate keys and sign messages much more efficiently than previous ideas.

Old Complex Steps
Old Slow Signing
New Quantum Circuits
Faster Key Generation
Simpler Multi-bit Signing