In classical cryptography, certified deletion is simply impossible. Since classical information can be copied any number of times easily. In quantum cryptography, certified deletion is possible because of theorems of quantum mechanics such as the quantum no-clone theorem, quantum superposition etc. In this paper, we show the PKE-CD (Public Key Encryption with Certified Deletion) scheme constructed in by Bartusek and Khurana in CRYPTO 2023 lack an important security property, which is important in practical applications. Then we show how to enhance this property, and construct a concrete scheme with this property. And we also discuss the relations between PKE-CD and other quantum cryptographic schemes such as quantum seal, quantum bit commitment etc.
In classical cryptography, certified deletion is simply impossible. Since classical information can be copied any number of times easily. In quantum cryptography, certified deletion is possible because of theorems of quantum mechanics such as the quantum no-clone theorem, quantum superposition etc. In this paper, we show the PKE-CD (Public Key Encryption with Certified Deletion) scheme constructed in by Bartusek and Khurana in CRYPTO 2023 lack an important security property, which is important in practical applications. Then we show how to enhance this property, and construct a concrete scheme with this property. And we also discuss the relations between PKE-CD and other quantum cryptographic schemes such as quantum seal, quantum bit commitment etc.
Quantum public-key encryption (PKE), where public-keys and/or ciphertexts can be quantum states, is an important primitive in quantum cryptography. Unlike classical PKE (e.g., RSA or ECC), quantum PKE can leverage quantumsecure cryptographic assumptions or the principles of quantum mechanics for security. It has great potential in providing for secure cryptographic systems under potentially weaker assumptions than is possible classically. In addition, it is of both practical and theoretical interest, opening the door to novel cryptographic systems not possible with classical information alone. While multiple quantum PKE schemes have been proposed, they require a large number of qubits acting coherently, and are not practical on current noisy quantum devices. In this paper, we design a practical quantum PKE scheme, taking into account the constraints of current NISQ devices. Specifically, we design a PKE scheme with quantum-classical public keys and classical ciphertexts, that is noise-resilient and only requires a small number of qubits acting coherently. In addition, our design provides tradeoffs in terms of efficiency and the number of qubits that are required.
Certified deletion allows a client to upload encrypted data to a server as a quantum state, then later request that the server delete their data and detect whether the server complies. If verification passes, then the data on the server will remain hidden even if the decryption key is later leaked. In publicly verifiable certified deletion, the verification key is published so that anyone may check for deletion compliance.
In this work, we give a general compiler to publicly verifiable certified deletion that allows the client to initially upload the *quantum* ciphertext using purely *classical* communication, assuming the post-quantum hardness of LWE in the plain model. Our approach can be applied to a wide variety of primitives, including commitments and public-key, attribute-based, identity-based, and fully-homomorphic encryption.
Moreover, our constructions allow the client to classically manage the encrypted data beyond just verifying its deletion. The classical client may non-destructively audit the ciphertext via a Proof of No Intrusion to check whether it has been leaked to a third party. The classical client may also retrieve the data while simultaneously verifying its deletion from the server. Thus, they do not have to choose between retrieving the data and protecting it against future key leakage.
As our core technical contribution, we give a classical-communication protocol and simulation technique that allows adapting purification-based security arguments for BB84-style states which are prepared through classical interaction. It makes the required purification available in a hybrid experiment, despite the classical transcript uniquely determining the prepared state in a real execution.
Certified deletion allows Alice to outsource data to Bob and, at a later time, obtain a verifiable guarantee that the file has been irreversibly deleted at her request. This functionality, while impossible using classical information alone, can be achieved using quantum information. Existing approaches rely either on one-time pad (OTP) encryption or on computational hardness assumptions that may be vulnerable to future advances in classical or quantum computing. In this work, we introduce and formalize hybrid encryption with certified deletion in the preprocessing model (pHE-CD) and propose two constructions. Each construction composes an information-theoretic key encapsulation mechanism (iKEM) with a data encapsulation mechanism that provides certified deletion (DEM-CD) security, offering different security guarantees depending on the properties of DEM-CD. When DEM-CD is one-time information-theoretically secure, the composition provides information-theoretic security for both encryption and certified deletion. When DEM-CD is computationally secure, the composed construction provides computationally secure (post-quantum) encryption and everlasting certified deletion, where confidentiality is computational until the deletion certificate is successfully verified. After successful verification, confidentiality becomes unconditional. That is, successful verification of the deletion certificate guarantees that the data has been removed information-theoretically from the adversary's view. Both pHE-CD constructions support the encryption of arbitrarily long messages. Construction 2 is key-efficient and uses a DEM-CD built from quantum coding and AES, providing quantum-safe security for encryption. We conclude by discussing the implications of our results and directions for future research.
Abstract Asymmetric encryption has some important applications in the field of communication. In classical computers, most public key encryption schemes are designed based on computational assumption. In other words, they can ensure computational security. When the computing power is large enough, it will pose a threat to these encryption schemes. We propose a quantum public key encryption scheme which based on properties of quantum physics. Our scheme realizes encryption and decryption with few resources and does not rely on any computational assumption. The key in our scheme consists of classical bits and qubits. Where the private key are classical bit and public key are qubits. The public key are generated through private key. We analyze the performance and security of the scheme. Our scheme ensures the information-theoretic secure and can be implemented easily.
Quantum information has the property that measurement is an inherently destructive process. This feature is most apparent in the principle of complementarity, which states that mutually incompatible observables cannot be measured at the same time. Recent work by Broadbent and Islam (TCC 2020) builds on this aspect of quantum mechanics to realize a cryptographic notion called certified deletion. While this remarkable notion enables a classical verifier to be convinced that a (private-key) quantum ciphertext has been deleted by an untrusted party, it offers no additional layer of functionality. In this work, we augment the proof-of-deletion paradigm with fully homomorphic encryption (FHE). We construct the first fully homomorphic encryption scheme with certified deletion - an interactive protocol which enables an untrusted quantum server to compute on encrypted data and, if requested, to simultaneously prove data deletion to a client. Our scheme has the desirable property that verification of a deletion certificate is public; meaning anyone can verify that deletion has taken place. Our main technical ingredient is an interactive protocol by which a quantum prover can convince a classical verifier that a sample from the Learning with Errors (LWE) distribution in the form of a quantum state was deleted. As an application of our protocol, we construct a Dual-Regev public-key encryption scheme with certified deletion, which we then extend towards a (leveled) FHE scheme of the same type. We introduce the notion of Gaussian-collapsing hash functions - a special case of collapsing hash functions defined by Unruh (Eurocrypt 2016) - and we prove the security of our schemes under the assumption that the Ajtai hash function satisfies a certain strong Gaussian-collapsing property in the presence of leakage.
Quantum information has the property that measurement is an inherently destructive process. This feature is most apparent in the principle of complementarity, which states that mutually incompatible observables cannot be measured at the same time. Recent work by Broadbent and Islam (TCC 2020) builds on this aspect of quantum mechanics to realize a cryptographic notion called certified deletion. While this remarkable notion enables a classical verifier to be convinced that a (private-key) quantum ciphertext has been deleted by an untrusted party, it offers no additional layer of functionality. In this work, we augment the proof-of-deletion paradigm with fully homomorphic encryption (FHE). We construct the first fully homomorphic encryption scheme with certified deletion -- an interactive protocol which enables an untrusted quantum server to compute on encrypted data and, if requested, to simultaneously prove data deletion to a client. Our scheme has the desirable property that verification of a deletion certificate is public; meaning anyone can verify that deletion has taken place. Our main technical ingredient is an interactive protocol by which a quantum prover can convince a classical verifier that a sample from the Learning with Errors (LWE) distribution in the form of a quantum state was deleted. As an application of our protocol, we construct a Dual-Regev public-key encryption scheme with certified deletion, which we then extend towards a (leveled) FHE scheme of the same type. We introduce the notion of Gaussian-collapsing hash functions -- a special case of collapsing hash functions defined by Unruh (Eurocrypt 2016) -- and we prove the security of our schemes under the assumption that the Ajtai hash function satisfies a certain strong Gaussian-collapsing property in the presence of leakage.