Efficient threshold function secret sharing with information-theoretic security
Function secret sharing (FSS) is a cryptographic primitive that is introduced by Boyle et al. (Eurocrypt 2015), motivated by application scenarios involving private access to large distributed data while minimising the overhead of communication, for example, private information retrieval. Informally...
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/145838 |
| _version_ | 1824453626131644416 |
|---|---|
| author | Luo, Jinglong Zhang, Liang Feng Lin, Fuchun Lin, Changlu |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Luo, Jinglong Zhang, Liang Feng Lin, Fuchun Lin, Changlu |
| author_sort | Luo, Jinglong |
| collection | NTU |
| description | Function secret sharing (FSS) is a cryptographic primitive that is introduced by Boyle et al. (Eurocrypt 2015), motivated by application scenarios involving private access to large distributed data while minimising the overhead of communication, for example, private information retrieval. Informally, an n-party FSS scheme splits a function f into n functions f 1 ,...,f n such that f = f 1 +...+ f n and every strict subset of the function shares hide f . Most of the known FSS constructions only have computational hiding, namely, the hiding property holds only against a computationally bounded adversary. We consider information-theoretic hiding in this work while allowing f to be recovered from t function shares and correspondingly, any (t - 1) function shares unconditionally hide f . Call it (t, n)-threshold function secret sharing ((t, n)-TFSS for short). Using information-theoretic tools and through a series of optimizations, we show that our (t, n)-TFSS have better performance than FSS in terms of communication complexity, a criterion that measures the efficiency of such protocols. Specifically, a (t, n)-TFSS scheme with communication complexity O(l) is designed in this paper and it is better than the existing FSS schemes with lowest communication complexity O(λl), where λ is the length of pseudo-random generator's seeds. In addition, the (t, n)-TFSS have an extra robustness property in the sense that even if up to (n - t) function shares are not available, the protocol still computes the function value at a given point correctly. |
| first_indexed | 2025-02-19T03:09:24Z |
| format | Journal Article |
| id | ntu-10356/145838 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:09:24Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1458382023-02-28T19:57:04Z Efficient threshold function secret sharing with information-theoretic security Luo, Jinglong Zhang, Liang Feng Lin, Fuchun Lin, Changlu School of Physical and Mathematical Sciences Science::Mathematics Function Secret Sharing Point Function Function secret sharing (FSS) is a cryptographic primitive that is introduced by Boyle et al. (Eurocrypt 2015), motivated by application scenarios involving private access to large distributed data while minimising the overhead of communication, for example, private information retrieval. Informally, an n-party FSS scheme splits a function f into n functions f 1 ,...,f n such that f = f 1 +...+ f n and every strict subset of the function shares hide f . Most of the known FSS constructions only have computational hiding, namely, the hiding property holds only against a computationally bounded adversary. We consider information-theoretic hiding in this work while allowing f to be recovered from t function shares and correspondingly, any (t - 1) function shares unconditionally hide f . Call it (t, n)-threshold function secret sharing ((t, n)-TFSS for short). Using information-theoretic tools and through a series of optimizations, we show that our (t, n)-TFSS have better performance than FSS in terms of communication complexity, a criterion that measures the efficiency of such protocols. Specifically, a (t, n)-TFSS scheme with communication complexity O(l) is designed in this paper and it is better than the existing FSS schemes with lowest communication complexity O(λl), where λ is the length of pseudo-random generator's seeds. In addition, the (t, n)-TFSS have an extra robustness property in the sense that even if up to (n - t) function shares are not available, the protocol still computes the function value at a given point correctly. Published version 2021-01-11T07:54:12Z 2021-01-11T07:54:12Z 2020 Journal Article Luo, J., Zhang, L. F., Lin, F., & Lin, C. (2020). Efficient threshold function secret sharing with information-theoretic security. IEEE Access, 8, 6523-6532. doi:10.1109/ACCESS.2019.2963677 2169-3536 https://hdl.handle.net/10356/145838 10.1109/ACCESS.2019.2963677 8 6523 6532 en IEEE Access © 2020 IEEE. This journal is 100% open access, which means that all content is freely available without charge to users or their institutions. All articles accepted after 12 June 2019 are published under a CC BY 4.0 license, and the author retains copyright. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, as long as proper attribution is given. application/pdf |
| spellingShingle | Science::Mathematics Function Secret Sharing Point Function Luo, Jinglong Zhang, Liang Feng Lin, Fuchun Lin, Changlu Efficient threshold function secret sharing with information-theoretic security |
| title | Efficient threshold function secret sharing with information-theoretic security |
| title_full | Efficient threshold function secret sharing with information-theoretic security |
| title_fullStr | Efficient threshold function secret sharing with information-theoretic security |
| title_full_unstemmed | Efficient threshold function secret sharing with information-theoretic security |
| title_short | Efficient threshold function secret sharing with information-theoretic security |
| title_sort | efficient threshold function secret sharing with information theoretic security |
| topic | Science::Mathematics Function Secret Sharing Point Function |
| url | https://hdl.handle.net/10356/145838 |
| work_keys_str_mv | AT luojinglong efficientthresholdfunctionsecretsharingwithinformationtheoreticsecurity AT zhangliangfeng efficientthresholdfunctionsecretsharingwithinformationtheoreticsecurity AT linfuchun efficientthresholdfunctionsecretsharingwithinformationtheoreticsecurity AT linchanglu efficientthresholdfunctionsecretsharingwithinformationtheoreticsecurity |