Homomorphic Secret Sharing for Low Degree Polynomials

Lai, Russell W. F.; Malavolta, Giulio; Schröder, Dominique

doi:10.1007/978-3-030-03332-3_11

Cited by 19 publications

(10 citation statements)

References 29 publications

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“…In this section, we implemented our scheme and got the running time of our scheme, and compared our scheme with the LMS scheme [21] in terms of efficiency.…”

Section: Performance Analysismentioning

confidence: 99%

“…We compare the efficiency of the scheme 2SVHSS with the LMS scheme [21] which supports polynomials of highest degree among all existing works, when the same number of servers are used. Because LMS is based on the k-HE assumption, we choose the homomorphic encryption scheme SH [10] to implement LMS.…”

Section: Comparisons With Lms [21]mentioning

confidence: 99%

“…We set those parameters according to the method of [24], and use the LWE estimator tool [1,32] to estimate the corresponding security parameters. The parameters of 2SVHSS and LMS [21] are shown in Table 3. It is fair to compare the two schemes under the same security parameters.…”

Section: Comparisons With Lms [21]mentioning

confidence: 99%

“…Most of the existing HSS schemes are designed for computing specific functions, such as the affine functions [2], the point functions [5], the selection functions [15,17], and the depth-2 boolean circuits [8]. Recent works [4,9,13,16,21] have focused on the construction of HSS schemes that support high-degree polynomial computations.…”

Section: Introductionmentioning

confidence: 99%

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Two-Server Verifiable Homomorphic Secret Sharing for High-Degree Polynomials

Chen

Zhang

2020

Lecture Notes in Computer Science

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Homomorphic secret sharing (HSS) allows multiple input clients to secret-share their data among multiple servers such that each server is able to locally compute a function on its shares to obtain a partial result and all partial results enable the reconstruction of the function's value on the outsourced data by an output client. The existing HSS schemes for high-degree polynomials either require a large number of servers or lack verifiability, which is essential for ensuring the correctness of the outsourced computations. In this paper, we propose a two-server verifiable HSS (VHSS) model and construct a scheme that supports the computation of high-degree polynomials. The degree of the outsourced polynomials can be as high as a polynomial in the system's security parameter. Despite of using only 2 servers, our VHSS ensures that each single server learns no information about the outsourced data and no single server is able to persuade the client to output a wrong function value. Our VHSS is significantly more efficient. When computing degree-7 polynomials, our scheme could be 3-10 times faster than the previously best construction.

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“…In this section, we implemented our scheme and got the running time of our scheme, and compared our scheme with the LMS scheme [21] in terms of efficiency.…”

Section: Performance Analysismentioning

confidence: 99%

Section: Comparisons With Lms [21]mentioning

confidence: 99%

Section: Comparisons With Lms [21]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two-Server Verifiable Homomorphic Secret Sharing for High-Degree Polynomials

Chen

Zhang

2020

Lecture Notes in Computer Science

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“…The communication complexity of an FSS scheme refers to the total amount of information that needs to be transmitted to complete this FSS scheme. This criterion captures the performance of FSS with respect to its applications to PIR and related scenarios such as homomorphic secret sharing [10]- [13] and fully homomorphic encryption [14], [15]. Most known constructions continued the pursuit of minimising the communication complexity within the computational security setting.…”

Section: Introductionmentioning

confidence: 99%

Efficient Threshold Function Secret Sharing With Information-Theoretic Security

et al. 2020

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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.

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