8.3 Quantum homomorphic encryption and blind computation

Quantum homomorphic encryption lets us perform computations on encrypted quantum data without decrypting it first. This preserves privacy and enables secure delegation of quantum computations to untrusted parties, opening up exciting possibilities for cloud quantum computing and secure multi-party quantum computation.

Blind quantum computation takes privacy a step further. It allows a client to delegate a quantum computation to a server while keeping everything hidden - the input, output, and even the nature of the computation itself. This is crucial for protecting sensitive data and proprietary algorithms.

Fundamentals of Quantum Homomorphic Encryption

Basic Concepts and Principles

Top images from around the web for Basic Concepts and Principles

• 

  Enabling New Generation Security Paradigm With Quantum Cryptography | Oriental Journal of ... View original

  Is this image relevant?

• 

  Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic ... View original

  Is this image relevant?

• 

  Enabling New Generation Security Paradigm With Quantum Cryptography | Oriental Journal of ... View original

  Is this image relevant?

• 

  Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic ... View original

  Is this image relevant?

1 of 2

Top images from around the web for Basic Concepts and Principles

• 

  Enabling New Generation Security Paradigm With Quantum Cryptography | Oriental Journal of ... View original

  Is this image relevant?

• 

  Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic ... View original

  Is this image relevant?

• 

  Enabling New Generation Security Paradigm With Quantum Cryptography | Oriental Journal of ... View original

  Is this image relevant?

• 

  Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic ... View original

  Is this image relevant?

1 of 2

• Quantum homomorphic encryption (QHE) enables performing computations on encrypted quantum data without decrypting it first, preserving the data's privacy
• QHE schemes allow secure delegation of quantum computations to untrusted parties as the computation is performed on encrypted data and the result is also encrypted
• The key challenge in designing QHE schemes is ensuring the encryption scheme is homomorphic with respect to a sufficient set of quantum gates to enable arbitrary computations
• Fully homomorphic encryption (FHE) schemes allow performing any computation on encrypted data
• Partially homomorphic encryption (PHE) schemes support a limited set of operations (addition or multiplication)

Applications and Use Cases

• QHE has applications in secure cloud quantum computing, enabling users to outsource quantum computations to remote servers while preserving data privacy
• Privacy-preserving quantum machine learning leverages QHE to train and evaluate quantum machine learning models on encrypted data
• Secure multi-party quantum computation allows multiple parties to jointly perform quantum computations on their private inputs without revealing the inputs to each other
• QHE can be used for secure quantum database queries, enabling users to search and retrieve information from encrypted quantum databases
• Quantum homomorphic signature schemes allow signing quantum states homomorphically, enabling verification of computations performed on signed quantum data

Security of Quantum Homomorphic Encryption

Security Properties and Requirements

• QHE schemes should provide semantic security, meaning an adversary cannot learn any information about the encrypted data, even with access to the ciphertext and auxiliary information
• The security of QHE schemes is often based on the indistinguishability of ciphertexts under chosen plaintext attacks (IND-CPA) or chosen ciphertext attacks (IND-CCA)
• QHE schemes must be resilient against quantum adversaries, considering the potential of quantum computers to break certain classical cryptographic assumptions
• The security of QHE schemes relies on the hardness of certain computational problems, such as the learning with errors (LWE) problem or the shortest vector problem (SVP) on lattices
• Quantum-resistant cryptographic primitives, such as lattice-based cryptography or quantum error-correcting codes, are used to construct secure QHE schemes

Challenges and Limitations

• The noise level in the ciphertext grows with each homomorphic operation, limiting the depth of computations that can be performed before the noise overwhelms the signal and decryption fails
• Bootstrapping, a technique used in FHE schemes to refresh the ciphertext and reduce the noise level, allows for unlimited computations but comes with a significant computational overhead
• The efficiency of QHE schemes, in terms of computation time and memory requirements, is a major challenge and an active area of research
• Implementing QHE schemes on noisy intermediate-scale quantum (NISQ) devices is challenging due to the limited coherence time and gate fidelity of current quantum hardware
• The scalability of QHE schemes to large-scale quantum computations is an open problem, requiring the development of efficient error correction and fault-tolerant quantum computation techniques

Blind Quantum Computation

Concept and Advantages

• Blind quantum computation allows a client to delegate a quantum computation to a server while keeping the input, output, and computation itself hidden from the server
• In a blind quantum computation protocol, the client prepares encrypted quantum states and sends them to the server, along with instructions for performing the computation
• The server performs the requested quantum operations on the encrypted states without learning anything about the actual data or the computation being performed
• Blind quantum computation provides a higher level of privacy compared to QHE, as the server does not even learn the nature of the computation being performed
• Advantages of blind quantum computation include preserving the privacy of sensitive data (medical records), protecting intellectual property (proprietary algorithms), and enabling secure outsourcing of quantum computations

Techniques and Protocols

• Blind quantum computation can be achieved through measuring-based quantum computation (MBQC), where the client prepares a set of single-qubit states and sends them to the server for measurement-based processing
• The use of quantum one-time pad allows the client to encrypt the input quantum states and decrypt the output states, while the server performs the computation on the encrypted states
• Verifiable blind quantum computation protocols enable the client to verify the correctness of the server's computation without learning the input or output states
• Secure delegated quantum computing protocols, such as the Broadbent-Fitzsimons-Kashefi (BFK) protocol, provide blindness and verifiability using trap qubits and measurement-based quantum computation
• Continuous-variable blind quantum computation protocols utilize continuous-variable quantum systems (coherent states) for encoding and processing quantum information

Protocols for Encrypted Quantum Data

Design Principles and Considerations

• Designing QHE protocols involves defining the encryption and decryption procedures, as well as the set of quantum gates that can be applied homomorphically
• The choice of the encryption scheme and the supported quantum gates depends on the desired level of homomorphism (fully or partially homomorphic) and the target applications
• QHE protocols should be designed to minimize the noise growth during homomorphic operations, enabling deeper computations before the need for noise reduction techniques
• The encryption and decryption procedures should be efficient and scalable, considering the limitations of current quantum hardware
• QHE protocols should be compatible with existing quantum error correction and fault-tolerance techniques to ensure reliable computations on noisy quantum devices

Security Analysis and Efficiency Evaluation

• Analyzing the security of QHE protocols requires proving that the scheme satisfies the desired security properties, such as semantic security or indistinguishability under chosen plaintext/ciphertext attacks
• The noise growth in the ciphertext during homomorphic operations should be carefully analyzed to determine the maximum depth of computations that can be performed before the noise becomes too high
• Techniques for noise management, such as bootstrapping or modulus switching, can be employed to extend the capabilities of QHE schemes
• The efficiency of QHE protocols, in terms of computation time, communication overhead, and memory requirements, should be evaluated and optimized to ensure practicality
• Blind quantum computation protocols can be analyzed for their security properties, such as blindness (the server learns nothing about the input, output, or computation) and verifiability (the client can verify the correctness of the server's computation)
• The resource requirements and scalability of blind quantum computation protocols should be assessed, considering the limitations of current quantum technologies and the potential for future improvements