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Distributing guess attack ccs2015 toolkit download mod#
In order to implement homomorphic computation on the ciphertext, they randomly split the secret key s into a pair of evaluation keys ( e k 1, e k 2 ) ∈ R 2 × 2 q such that s = ( e k 1 + e k 2 ) mod q. The input clients use PKE-NLD and the public key p k to encrypt x ⋅ s as C x = ( c x ⋅ 1, c x ⋅ s ) ∈ R 2 × 2 q, without knowing the secret key s. Informally, a public-key encryption scheme supports nearly linear decryption for a message x ∈ R p if the secret key is s = ( s 1, s 2 ) = ( 1, s ) ∈ R 2 p, and for any ciphertext c ∈ R 2 q encrypting x, ⟨ s, c ⟩ = ( q / p ) ⋅ x + e mod q for some “small” noise e ∈ R. Let R = Z / ( x N + 1 ), where p, q ∈ N, p | q and 1 ≪ p ≪ q. The core technique of the HSS scheme of is a public-key encryption scheme supporting nearly linear decryption (PKE-NLD). The degrees of these polynomials can be as high as a polynomial in the system’s security parameter.Īchieving verifiability in two-server HSS for high-degree polynomials allows us to distinguish between this work and the existing ones. In the proposed model we construct a 2SVHSS scheme that allows theĬomputation of polynomials over the outsourced data.
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This property is essential for HSS’s applications in outsourcing computation. The compactness property requires that the output client’s workload in a protocol execution should be substantially less than that required by the native computation of the function.
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This property is specifically interesting when the output client is not one of the input clients. The context hiding property requires that the output client learns no more information about the outsourced data than what is implied by the function value. The verifiability requires that no malicious server is able to persuade the output client to reconstruct a wrong function value. The semantic security requires that each server learns no information about the outsourced data. Is correctly executed, the output client will always reconstruct The correctness property requires that whenever the scheme On the outsourced data, each server performs a computation on its own shares and produces a partial result finally, the output client reconstructs the function value from all partial results.Ī 2SVHSS scheme in our model should satisfy the properties of correctness, semantic security, verifiability, context hiding and compactness. Each input client uses a public key to encrypt its data as shares to the servers upon the request of computing a function Our model involves three kinds of parties: a set of input clients, a set of servers, and an output client. In this paper, we propose a two-server verifiable homomorphic secret sharing (2SVHSS) model. Recent works have focused on the construction of HSS schemes that support high-degree polynomial computations. Specific functions, such as the affine functions, the point functions, the selection functions, and the depth-2 boolean circuits. Most of the existing HSS schemes are designed for computing Upon request each server is able to compute a partial result andĪll partial results suffice to reconstruct the correct function value by allows the input clients to secret-share their data among multiple servers such that Īs a multi-server counterpart of HE that is more efficient, the HSS of Boyle et al. Impractical from the performance perspective. Although the efficiency of FHE has been significantly improved Gentry proposed the first fully homomorphic encryption (FHE) scheme that allows the computation of any boolean circuits on encrypted data. The early HE schemes only support degree-1 computations on the encrypted data. Servers to compute a function f on the ciphertexts E n c ( x 1 ), …, E n c ( x n ) to get a ciphertext of the function value y = f ( x 1, …, x n ). The homomorphic encryption (HE), which allows the cloud Privacy of the data in outsourcing computation is by using WhenĬomputing degree-7 polynomials, our scheme could be 3-10 times faster than the Our VHSS is significantly more efficient. The outsourced data and no single server is able to persuade the client to Despite of using onlyĢ servers, our VHSS ensures that each single server learns no information about High as a polynomial in the system's security parameter. The degree of the outsourced polynomials can be as (VHSS) model and construct a scheme that supports the computation of In this paper, we propose a two-server verifiable HSS 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 Partial results enable the reconstruction of the function's value on the Locally compute a function on its shares to obtain a partial result and all Secret-share their data among multiple servers such that each server is able to Homomorphic secret sharing (HSS) allows multiple input clients to