Expand-and-Randomize: An Algebraic Approach to Secure Computation
We consider the secure computation problem in a minimal model, where Alice and Bob each holds an input and wish to securely compute a function of their inputs at Carol without revealing any additional information about the inputs. For this minimal secure computation problem, we propose a novel codin...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/11/1461 |
| _version_ | 1797510453294792704 |
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| author | Yizhou Zhao Hua Sun |
| author_facet | Yizhou Zhao Hua Sun |
| author_sort | Yizhou Zhao |
| collection | DOAJ |
| description | We consider the secure computation problem in a minimal model, where Alice and Bob each holds an input and wish to securely compute a function of their inputs at Carol without revealing any additional information about the inputs. For this minimal secure computation problem, we propose a novel coding scheme built from two steps. First, the function to be computed is <i>expanded</i> such that it can be recovered while additional information might be leaked. Second, a <i>randomization</i> step is applied to the expanded function such that the leaked information is protected. We implement this expand-and-randomize coding scheme with two algebraic structures—the finite field and the modulo ring of integers, where the <i>expansion</i> step is realized with the <i>addition</i> operation and the <i>randomization</i> step is realized with the <i>multiplication</i> operation over the respective algebraic structures. |
| first_indexed | 2024-03-10T05:31:42Z |
| format | Article |
| id | doaj.art-a121a166e25c46cda4c0afd1ad5e897e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T05:31:42Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-a121a166e25c46cda4c0afd1ad5e897e2023-11-22T23:15:18ZengMDPI AGEntropy1099-43002021-11-012311146110.3390/e23111461Expand-and-Randomize: An Algebraic Approach to Secure ComputationYizhou Zhao0Hua Sun1Department of Electrical Engineering, University of North Texas, Denton, TX 76203, USADepartment of Electrical Engineering, University of North Texas, Denton, TX 76203, USAWe consider the secure computation problem in a minimal model, where Alice and Bob each holds an input and wish to securely compute a function of their inputs at Carol without revealing any additional information about the inputs. For this minimal secure computation problem, we propose a novel coding scheme built from two steps. First, the function to be computed is <i>expanded</i> such that it can be recovered while additional information might be leaked. Second, a <i>randomization</i> step is applied to the expanded function such that the leaked information is protected. We implement this expand-and-randomize coding scheme with two algebraic structures—the finite field and the modulo ring of integers, where the <i>expansion</i> step is realized with the <i>addition</i> operation and the <i>randomization</i> step is realized with the <i>multiplication</i> operation over the respective algebraic structures.https://www.mdpi.com/1099-4300/23/11/1461secure computationcapacityalgebraic codes |
| spellingShingle | Yizhou Zhao Hua Sun Expand-and-Randomize: An Algebraic Approach to Secure Computation Entropy secure computation capacity algebraic codes |
| title | Expand-and-Randomize: An Algebraic Approach to Secure Computation |
| title_full | Expand-and-Randomize: An Algebraic Approach to Secure Computation |
| title_fullStr | Expand-and-Randomize: An Algebraic Approach to Secure Computation |
| title_full_unstemmed | Expand-and-Randomize: An Algebraic Approach to Secure Computation |
| title_short | Expand-and-Randomize: An Algebraic Approach to Secure Computation |
| title_sort | expand and randomize an algebraic approach to secure computation |
| topic | secure computation capacity algebraic codes |
| url | https://www.mdpi.com/1099-4300/23/11/1461 |
| work_keys_str_mv | AT yizhouzhao expandandrandomizeanalgebraicapproachtosecurecomputation AT huasun expandandrandomizeanalgebraicapproachtosecurecomputation |