Secure Outsourcing of Matrix Determinant Computation under the Malicious Cloud.

Area of Science:

• Computational science and engineering
• Cloud computing security
• Cryptography

Background:

• Large matrix determinant computation is crucial in big data science and engineering.
• Cloud computing offers resources but poses security risks like data privacy breaches and incorrect computations.
• Existing secure outsourcing methods often require multiple verification rounds, increasing local computation burden.

Purpose of the Study:

• To propose a secure outsourcing algorithm for computing the determinant of large matrices in a malicious cloud environment.
• To enhance data privacy and ensure computational integrity against cloud threats.
• To reduce the local computation burden for resource-constrained devices.

Main Methods:

• The algorithm employs row/column permutation and other transformations to protect original matrix privacy.
• A novel single-round verification method is introduced to detect malicious cheating without compromising accuracy.
• Theoretical analysis and experimental evaluations are conducted to validate the algorithm's performance.

Main Results:

• The proposed algorithm effectively protects matrix privacy through data transformation techniques.
• The single-round verification method achieves high cheating detectability.
• Experimental results show improved efficiency for local users compared to existing methods across various matrix dimensions.

Conclusions:

• The developed algorithm provides a secure and efficient solution for outsourced large matrix determinant computation.
• It balances privacy protection, cheating detectability, and reduced local computation overhead.
• This approach is suitable for resource-constrained devices leveraging cloud computing capabilities.