On black-box separations of quantum digital signatures from pseudorandom states

• URL: http://arxiv.org/abs/2402.08194v1
• Date: Tue, 13 Feb 2024 03:36:35 GMT
• Title: On black-box separations of quantum digital signatures from pseudorandom states
• Authors: Andrea Coladangelo and Saachi Mutreja
• Abstract summary: We show that there $textitdoes not$ exist a black-box construction of a quantum digital signatures scheme. Our result complements that of Morimae and Yamakawa (2022), who described a $textitone-time$ secure QDS scheme with classical signatures.
• Score: 1.9254132307399263
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is well-known that digital signatures can be constructed from one-way functions in a black-box way. While one-way functions are essentially the minimal assumption in classical cryptography, this is not the case in the quantum setting. A variety of qualitatively weaker and inherently quantum assumptions (e.g. EFI pairs, one-way state generators, and pseudorandom states) are known to be sufficient for non-trivial quantum cryptography. While it is known that commitments, zero-knowledge proofs, and even multiparty computation can be constructed from these assumptions, it has remained an open question whether the same is true for quantum digital signatures schemes (QDS). In this work, we show that there $\textit{does not}$ exist a black-box construction of a QDS scheme with classical signatures from pseudorandom states with linear, or greater, output length. Our result complements that of Morimae and Yamakawa (2022), who described a $\textit{one-time}$ secure QDS scheme with classical signatures, but left open the question of constructing a standard $\textit{multi-time}$ secure one.

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