🤖 AI Summary
This work proposes the first quantum one-time signature scheme implemented at the circuit level without computational assumptions, supporting applications such as delegated signing, secure token transfer, and publicly verifiable randomness. The scheme employs a classical public key and quantum secret key structure, leveraging superpositions of random affine cosets, puncturable pseudorandom functions, and coset membership testing circuits to achieve security against both classical and quantum polynomial-time adversaries while requiring only classical verification. It achieves a logical qubit count of Θ(κ log r + n + l) and gate complexity of Θ(n³ + nl), with a detailed quantification of quantum resource overhead under varying parameters, thereby balancing security and efficiency.
📝 Abstract
We provide a pre-obfuscation circuit-level implementation of an efficient one shot signature scheme, which has known applications to delegated signatures, secured token transfer, and publicly verifiable randomness. The algorithm consists of two stages: a key generation stage where a classical public key/quantum secret key pair is produced, and a signing stage where the quantum secret key is processed with a message string to produce a classical signature. There is no algorithmic error in the construction and the signed message can be efficiently checked by a classical verifier. Our scheme works by preparing a superposition over elements of a random affine coset determined by the output of a puncturable pseudorandom function, together with a circuit that tests coset membership. The logical qubit number scales like $Θ( κ\log(r) + n + l)$ and the gate complexity scales like $Θ(n^3 + nl)$, where $r$ is the public key size, $n+l$ is the signature size, $l$ is the message size, and $κ= Ω(n)$ is the cryptographic security parameter. We provide explicit qubit and gate counts for varying $n$ and identify the circuit components where obfuscation would be required for security against classical and quantum polynomial time attacks.