Abstract
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 has been 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.
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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 functions. These two schemes are privately verifiable.
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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.
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Notes
- 1.
We note that if the adversary is given the decryption key before the deletion, it can decrypt the ciphertext to obtain the message and keep it even after the deletion, but such an “attack” is unavoidable.
- 2.
- 3.
A recent work by Coladangelo, Majenz, and Poremba [CMP20] studied what is called “simultaneous one-way to hiding lemma”, but their setting is different from ours and their lemma cannot be used in our setting.
- 4.
We require \(\mathsf {Enc}\) to satisfy the RNC security due to a similar reason to that in Sect. 1.3, which we omit to explain here.
- 5.
In the actual construction, there is an additional component that is needed for preventing an adversary from decrypting the ciphertext before outputting a valid deletion certificate without the decryption key. This is just a security as standard PKE and can be added easily. Thus, we omit this and focus on the security after outputting a valid deletion certificate.
- 6.
We note that a combination of one-shot signatures and extractable witness encryption appeared in the work of Georgiou and Zhandry [GZ20] in a related but different context.
- 7.
We can also take \(S\subseteq [2n]\) such that \(|S|=n\), but we do as above just for convenience in the proof.
- 8.
Indeed,
for \(i\in S\). - 9.
If \(S'=\bot \) or \(K'=\bot \), output \(\bot \).
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Acknowledgements
TM is supported by the Moonshot R&D JPMJMS2061-5-1-1, MEXT Q-LEAP, JST FOREST, JST PRESTO No. JPMJPR176A, and the Grant-in-Aid for Scientific Research (B) No. JP19H04066 of JSPS.
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Hiroka, T., Morimae, T., Nishimaki, R., Yamakawa, T. (2021). Quantum Encryption with Certified Deletion, Revisited: Public Key, Attribute-Based, and Classical Communication. In: Tibouchi, M., Wang, H. (eds) Advances in Cryptology – ASIACRYPT 2021. ASIACRYPT 2021. Lecture Notes in Computer Science(), vol 13090. Springer, Cham. https://doi.org/10.1007/978-3-030-92062-3_21
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