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 within the quantum random oracle model (QROM), assuming the existence of post-quantum secure one-way functions (pq-OWFs). 2) By utilizing verification keys that evolve over time, we eliminate the need for the random oracle 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。在这项工作中，我们挑战了这一观念，并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。我们的贡献可总结如下：1）引入了时间依赖性（TD）签名概念，其中量子消息的签名依赖于签署时间，而验证过程依赖于签名接收时间。我们在量子随机预言机模型（QROM）中构建了这一原语，假设存在抗量子安全单向函数（pq-OWF）。2）通过利用随时间演变的验证密钥，我们在构造中消除了对随机预言机的需求，从而实现了具有动态验证密钥的、基于pq-OWF的TD签名。3）进一步考虑有界量子存储模型，其中对手的量子记忆能力受限。我们证明在此模型中，量子消息可实现信息论安全性的签名。此外，我们仅依赖pq-OWF便利用TD签名实现了以下目标：(a) 设计了一种具有可抵抗恶意篡改的认证量子公钥的公钥加密方案。(b) 提出了一种新颖的TD公钥量子货币方案。