Abstract: A function is decomposed into a plurality of function shares. The function returns a Boolean result based on whether an input y satisfies a query on a data set. The function shares hide the function from non-collaborating entities that separately execute the function shares. Each of the functions shares are sent to one of a plurality of servers having a same data set. The function shares are executed on the data set at the servers to obtain a respective plurality of shares. A conditional disclosure of secrets operation is simulated on the shares and the input y. The conditional disclosure of secrets operation uses a secret known to at least one of the servers, and further uses a source of randomness shared between the servers. A Boolean value corresponding to the Boolean result is returned based on the conditional disclosure of secrets operation returning the secret.

Abstract: A function secret sharing (FSS) scheme that facilitates multiple evaluations of a secret function. The FSS scheme includes a function share based on a secret function and at least one key of a key-homomorphic pseudo random function (PRF). At least one key and a function share are provided to each party in the FSS scheme. In turn, each party may generate an output share comprising a function share output evaluated at a function input and a masking component generated based on the at least one key in relation to the key-homomorphic PRF. In turn, the output shares of each participating party may be combined to evaluate the secret function. The FSS scheme facilitates multiple evaluations of the secret function without leaking information regarding the secret function.

Abstract: Polynomial function secret sharing provides for computation of reconstruction share results for a polynomial function on an input. An allocatable share of the polynomial function is received at a computing system of the share result computation systems. The allocatable share is generated from the polynomial function. Each of the allocatable shares is distributed to a unique share result computation system of the share result computation systems. Each allocatable share includes a share element for each coefficient in the polynomial function, wherein the share elements for a coefficient across the share result computation systems summing to the coefficient. A reconstruction share result is generated at the computing system by computing a dot product of the input and the allocatable share received by the computing system. A combination of the reconstruction share results generated by the share result computation systems yields a reconstructed result of the polynomial function on the input.

Abstract: A function secret sharing (FSS) scheme that facilitates multiple evaluations of a secret function. The FSS scheme includes a function share based on a secret function and at least one key of a key-homomorphic pseudo random function (PRF). At least one key and a function share are provided to each party in the FSS scheme. In turn, each party may generate an output share comprising a function share output evaluated at a function input and a masking component generated based on the at least one key in relation to the key-homomorphic PRF. In turn, the output shares of each participating party may be combined to evaluate the secret function. The FSS scheme facilitates multiple evaluations of the secret function without leaking information regarding the secret function.

Abstract: A function is decomposed into a plurality of function shares. The function returns a Boolean result based on whether an input y satisfies a query on a data set. The function shares hide the function from non-collaborating entities that separately execute the function shares. Each of the functions shares are sent to one of a plurality of servers having a same data set. The function shares are executed on the data set at the servers to obtain a respective plurality of shares. A conditional disclosure of secrets operation is simulated on the shares and the input y. The conditional disclosure of secrets operation uses a secret known to at least one of the servers, and further uses a source of randomness shared between the servers. A Boolean value corresponding to the Boolean result is returned based on the conditional disclosure of secrets operation returning the secret.