Certified Everlasting Zero-Knowledge Proof for QMA
In known constructions of classical zero-knowledge protocols for NP, either of zero-knowledge or soundness holds only against computationally bounded adversaries. Indeed, achieving both statistical zero-knowledge and statistical soundness at the same time with classical verifier is impossible for NP unless the polynomial-time hierarchy collapses, and it is also believed to be impossible even with a quantum verifier. In this work, we introduce a novel compromise, which we call the certified everlasting zero-knowledge proof for QMA. It is a computational zero-knowledge proof for QMA, but the verifier issues a classical certificate that shows that the verifier has deleted its quantum information. If the certificate is valid, even an unbounded malicious verifier can no longer learn anything beyond the validity of the statement. We construct a certified everlasting zero-knowledge proof for QMA. For the construction, we introduce a new quantum cryptographic primitive, which we call commitment with statistical binding and certified everlasting hiding, where the hiding property becomes statistical once the receiver has issued a valid certificate that shows that the receiver has deleted the committed information. We construct commitment with statistical binding and certified everlasting hiding from quantum encryption with certified deletion by Broadbent and Islam [TCC 2020] (in a black-box way), and then combine it with the quantum sigma-protocol for QMA by Broadbent and Grilo [FOCS 2020] to construct the certified everlasting zero-knowledge proof for QMA. Our constructions are secure in the quantum random oracle model. Commitment with statistical binding and certified everlasting hiding itself is of independent interest, and there will be many other useful applications beyond zero-knowledge.
Quantum Encryption with Certified Deletion, Revisited: Public Key, Attribute-Based, and Classical Communication 📺
Broadbent and Islam (TCC '20) proposed a quantum cryptographic primitive called quantum encryption with certified deletion. In this primitive, a receiver in possession of a quantum ciphertext can generate a classical certificate that the encrypted message is deleted. Although their construction is information-theoretically secure, it is limited to the setting of one-time symmetric key encryption (SKE), where a sender and receiver have to share a common key in advance and the key can be used only once. Moreover, the sender has to generate a quantum state and send it to the receiver over a quantum channel in their construction. Deletion certificates are privately verifiable, which means a verification key for a certificate must be kept secret, in the definition by Broadbent and Islam. However, we can also consider public verifiability. In this work, we present various constructions of encryption with certified deletion. - Quantum communication case: We achieve (reusable-key) public key encryption (PKE) and attribute-based encryption (ABE) with certified deletion. Our PKE scheme with certified deletion is constructed assuming the existence of IND-CPA secure PKE, and our ABE scheme with certified deletion is constructed assuming the existence of indistinguishability obfuscation and one-way function. These two schemes are privately verifiable. - Classical communication case: We also achieve interactive encryption with certified deletion that uses only classical communication. We give two schemes, a privately verifiable one and a publicly verifiable one. The former is constructed assuming the LWE assumption in the quantum random oracle model. The latter is constructed assuming the existence of one-shot signatures and extractable witness encryption.