Invertible polynomial representation for private set operationsopen access
- Authors
- Cheon, J.H.; Hong, H.; Lee, H.T.
- Issue Date
- Jan-2014
- Publisher
- Springer Verlag
- Keywords
- Polynomial factorization; Polynomial representation; Privacy-preserving set union; Root finding
- Citation
- Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), v.8565, pp 277 - 292
- Pages
- 16
- Journal Title
- Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
- Volume
- 8565
- Start Page
- 277
- End Page
- 292
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/64762
- DOI
- 10.1007/978-3-319-12160-4_17
- ISSN
- 0302-9743
1611-3349
- Abstract
- In many private set operations, a set is represented by a polynomial over a ring ℤσfor a composite integer σ, where ℤσis the message space of some additive homomorphic encryption. While it is useful for implementing set operations with polynomial additions and multiplications, it has a limitation that it is hard to recover a set from a polynomial due to the hardness of polynomial factorization over ℤσ. We propose a new representation of a set by a polynomial over ℤσ, in which σ is a composite integer with known factorization but a corresponding set can be efficiently recovered from a polynomial except negligible probability. Since ℤσ[x] is not a unique factorization domain, a polynomial may be written as a product of linear factors in several ways. To exclude irrelevant linear factors, we introduce a special encoding function which supports early abort strategy. Our representation can be efficiently inverted by computing all the linear factors of a polynomial in ℤσ[x] whose roots locate in the image of the encoding function. As an application of our representation, we obtain a constant-round private set union protocol. Our construction improves the complexity than the previous without honest majority.
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