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，对量子消息进行签名一直被认为是不可能的。在本工作中，我们挑战了这一观念，并提出了三种创新的方法来对量子消息进行签名，这些方法首次确保了具有公开可验证性的真实性。我们的贡献可总结如下：1) 我们引入了时间依赖（TD）签名的概念，其中量子消息的签名依赖于签名时间，而验证过程依赖于签名接收时间。我们基于后量子安全单向函数（pq-OWFs）和时间锁谜题（TLPs）的存在性构造了这一原语。2) 通过利用随时间演化的验证密钥，我们在构造中消除了对TLPs的需求。这导致了具有动态验证密钥的、基于pq-OWFs的TD签名。3) 随后，我们考虑了有界量子存储模型，其中对手的量子存储器容量受到限制。我们证明，在该模型下，量子消息可以以信息论安全性被签名。此外，我们利用TD签名实现了以下目标，仅依赖于pq-OWFs：(a) 我们设计了一种公钥加密方案，其具有可认证的量子公钥，能够抵抗敌方的篡改。(b) 我们提出了一种新颖的TD公钥量子货币方案。