A New Quantum Private Protocol for Set Intersection Cardinality Based on a Quantum Homomorphic Encryption Scheme for...

Area of Science:

• Quantum Computing
• Cryptography
• Data Security

Background:

• Set Intersection Cardinality (SI-CA) is crucial for data mining and analysis but faces scalability challenges with big data.
• Repeated execution of traditional SI-CA protocols is computationally intensive for large datasets.
• Existing methods struggle to efficiently handle the intersection cardinality of massive private sets.

Purpose of the Study:

• To propose a novel Private Set Intersection Cardinality (PSI-CA) protocol to alleviate computational pressure.
• To leverage a quantum homomorphic encryption scheme for efficient and secure set intersection cardinality computation.
• To enable secure comparison of quantum sequences representing private sets.

Main Methods:

• Developed a Private Set Intersection Cardinality (PSI-CA) protocol utilizing a quantum homomorphic encryption scheme for the Toffoli gate.
• Parties encode private sets into quantum sequences and encrypt them using the proposed quantum homomorphic encryption.
• A semi-honest third party uses the Toffoli gate and decrypted keys to determine quantum sequence equality.

Main Results:

• Successfully simulated the quantum homomorphic encryption scheme for the Toffoli gate on two quantum bits.
• The simulation was conducted using the IBM Quantum Experience platform, validating the scheme's functionality.
• Demonstrated that the scheme can effectively compute the corresponding function on two quantum sequences.

Conclusions:

• The proposed quantum homomorphic encryption-based PSI-CA protocol offers a viable solution for big data scenarios.
• This quantum approach reduces the execution pressure associated with traditional repeated SI-CA protocols.
• The scheme provides a secure and efficient method for determining set intersection cardinality in a distributed manner.