Signing quantum messages has long been considered impossible even under computational assumptions. In this work, we challenge this notion and provide three innovative approaches to sign quantum messages that are the first to ensure authenticity with public verifiability. Our contributions can be summarized as follows: 1) We introduce the concept of time-dependent (TD) signatures, where the signature of a quantum message depends on the time of signing and the verification process depends on the time of the signature reception. We construct this primitive assuming the existence of post-quantum secure one-way functions (pq-OWFs) and time-lock puzzles (TLPs). 2) By utilizing verification keys that evolve over time, we eliminate the need for TLPs in our construction. This leads to TD signatures from pq-OWFs with dynamic verification keys. 3) We then consider the bounded quantum storage model, where adversaries are limited with respect to their quantum memories. We show that quantum messages can be signed with information-theoretic security in this model. Moreover, we leverage TD signatures to achieve the following objectives, relying solely on pq-OWFs: (a) We design a public key encryption scheme featuring authenticated quantum public keys that resist adversarial tampering. (b) We present a novel TD public-key quantum money scheme.

翻译：长期以来，即使在计算假设下，签署量子消息也被认为是不可能的。本研究挑战了这一观念，提出了三种创新方法来实现量子消息的签署，首次确保了可公开验证的真实性。我们的贡献可概括如下：1) 引入时间依赖（TD）签名的概念，其中量子消息的签名取决于签署时间，而验证过程取决于签名接收时间。我们假设存在后量子安全单向函数（pq-OWF）和时间锁谜题（TLP）来构建这一原语。2) 通过利用随时间演化的验证密钥，我们消除了构建中对TLP的需求，从而得到了基于pq-OWF的动态验证密钥TD签名。3) 进一步考虑有界量子存储模型，即对手的量子记忆能力受限。我们证明在此模型下，量子消息可实现信息论安全性的签署。此外，仅依赖pq-OWF，我们利用TD签名实现了以下目标：(a) 设计了一种公钥加密方案，其具备可抵御对手篡改的认证量子公钥；(b) 提出了一种新颖的TD公钥量子货币方案。