Outsourcing computing of large matrix Jordan decomposition. (English) Zbl 1435.94147
Summary: The Jordan decomposition of matrix is a typical scientific and engineering computational task, but such computation involves enormous computing resources for large matrices, which is burdensome for the resource-limited clients. Cloud computing enables computational resource-limited clients to economically outsource such problems to the cloud server. However, outsourcing Jordan decomposition of large-scale matrix to the cloud brings great security concerns and challenges since the matrices usually contain sensitive information. In this paper, we present a secure, verifiable, efficient, and privacy preserving algorithm for outsourcing Jordan decomposition of large-scale matrix. Security analysis shows that our algorithm is practically secure. Efficient verification algorithm is used to verify the results returned from the cloud.
MSC:
| 94A62 | Authentication, digital signatures and secret sharing |
| 65F99 | Numerical linear algebra |
| 68P25 | Data encryption (aspects in computer science) |
| 15B33 | Matrices over special rings (quaternions, finite fields, etc.) |
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