Abstract: A secure multi-party computation implements real number arithmetic using modular integer representation on the backend. As part of the implementation, a secret shared value jointly stored by multiple parties in a first modular representation is cast into a second modular representation having a larger most significant bit. The parties use a secret shared masking value in the first representation, the range of which is divided into two halves, to mask and reveal a sum of the secret shared value and the secret shared masking value. The parties use a secret shared bit that identifies the half of the range that contains the masking value, along with the sum to collaboratively construct a set of secret shares representing the secret shared value in the second modular format. In contrast with previous work, the disclosed solution eliminates a non-zero probability of error without sacrificing efficiency or security.

Abstract: A secure multi-party computing system performs a multi-pivot partial sorting operation on a secret shared array of values. The use of multiple pivots supports efficient computations in a multi-party computation setting. Partial sorting determines percentile values without the need for a full sort. The secret shared array is first permuted by a secret random permutation. A multi-pivot sort, which can be a partial sort, is performed on the permuted array to obtain a public sorting permutation. The multi-pivot sort uses oblivious comparisons that produce secret shared Boolean indications of whether one secret shared value is less than another. The Boolean indications are revealed and used to produce the public sorting permutation, which in turn, is applied to the secret random permutation to obtain a secret shared sorting permutation. The secret shared sorting permutation is then applied to the secret shared array to obtain a sorted secret shared result.

Abstract: A method for performing privacy-preserving or secure multi-party computations enables multiple parties to collaborate to produce a shared result while preserving the privacy of input data contributed by individual parties. The method can produce a result with a specified high degree of precision or accuracy in relation to an exactly accurate plaintext (non-privacy-preserving) computation of the result, without unduly burdensome amounts of inter-party communication. The multi-party computations can include a Fourier series approximation of a continuous function or an approximation of a continuous function using trigonometric polynomials, for example, in training a machine learning classifier using secret shared input data.

Abstract: An efficient method of feature selection for regression models can be implemented in a privacy-preserving manner in a multi-party computation setting. In accordance with various embodiments, the method takes as input data a feature matrix, a dependent variable vector, and an external feature matrix from which a feature is to be selected for addition to a regression model. Some or all of the input data can include private data that can be secret shared during the method so as not to disclose the private data to other parties. Based on two heuristic assumptions, the method determines numerators and denominators for a t-statistics vector in multi-party computations and then calculates the t-statistics vector. In determining the numerators and denominators, the method can determine a baseline Hessian matrix and a vector of predictions. A feature represented in the external feature matrix is then selected based on the calculated t-statistics vector.

Abstract: An oblivious comparison method takes as input two secret shared numerical values x and y and outputs a secret shared bit that is the result of the comparison of x and y (e.g. 1 if x<y and 0 otherwise). The method uses secure multi-party computation, allowing multiple parties to collaboratively perform the comparison while keeping the inputs private and revealing only the result. The two secret shared values are subtracted to compute a secret shared result, the sign of which indicates the result of the comparison. The method decomposes the secret shared result into a masked Boolean representation and then performs a bit-wise addition of the mask and the masked result. Through the bit-wise addition the method can extract a secret shared representation of the most significant bit, which indicates the sign of the result, without revealing the result itself.

Abstract: A secure multi-party computation implements real number arithmetic using modular integer representation on the backend. As part of the implementation, a secret shared value jointly stored by multiple parties in a first modular representation is cast into a second modular representation having a larger most significant bit. The parties use a secret shared masking value in the first representation, the range of which is divided into two halves, to mask and reveal a sum of the secret shared value and the secret shared masking value. The parties use a secret shared bit that identifies the half of the range that contains the masking value, along with the sum to collaboratively construct a set of secret shares representing the secret shared value in the second modular format. In contrast with previous work, the disclosed solution eliminates a non-zero probability of error without sacrificing efficiency or security.

Abstract: A secure multi-party computation implements real number arithmetic using modular integer representation on the backend. As part of the implementation, a secret shared value jointly stored by multiple parties in a first modular representation is cast into a second modular representation having a larger most significant bit. The parties use a secret shared masking value in the first representation, the range of which is divided into two halves, to mask and reveal a sum of the secret shared value and the secret shared masking value. The parties use a secret shared bit that identifies the half of the range that contains the masking value, along with the sum to collaboratively construct a set of secret shares representing the secret shared value in the second modular format. In contrast with previous work, the disclosed solution eliminates a non-zero probability of error without sacrificing efficiency or security.

Abstract: A method for performing privacy-preserving or secure multi-party computations enables multiple parties to collaborate to produce a shared result while preserving the privacy of input data contributed by individual parties. The method can produce a result with a specified high degree of precision or accuracy in relation to an exactly accurate plaintext (non-privacy-preserving) computation of the result, without unduly burdensome amounts of inter-party communication. The multi-party computations can include a Fourier series approximation of a continuous function or an approximation of a continuous function using trigonometric polynomials, for example, in training a machine learning classifier using secret shared input data.

Abstract: A secure multi-party computation implements real number arithmetic using modular integer representation on the backend. As part of the implementation, a secret shared value jointly stored by multiple parties in a first modular representation is cast into a second modular representation having a larger most significant bit. The parties use a secret shared masking value in the first representation, the range of which is divided into two halves, to mask and reveal a sum of the secret shared value and the secret shared masking value. The parties use a secret shared bit that identifies the half of the range that contains the masking value, along with the sum to collaboratively construct a set of secret shares representing the secret shared value in the second modular format. In contrast with previous work, the disclosed solution eliminates a non-zero probability of error without sacrificing efficiency or security.

Abstract: A method for performing privacy-preserving or secure multi-party computations enables multiple parties to collaborate to produce a shared result while preserving the privacy of input data contributed by individual parties. The method can produce a result with a specified high degree of precision or accuracy in relation to an exactly accurate plaintext (non-privacy-preserving) computation of the result, without unduly burdensome amounts of inter-party communication. The multi-party computations can include a Fourier series approximation of a continuous function or an approximation of a continuous function using trigonometric polynomials, for example, in training a machine learning classifier using secret shared input data.

Abstract: A method for performing privacy-preserving or secure multi-party computations enables multiple parties to collaborate to produce a shared result while preserving the privacy of input data contributed by individual parties. The method can produce a result with a specified high degree of precision or accuracy in relation to an exactly accurate plaintext (non-privacy-preserving) computation of the result, without unduly burdensome amounts of inter-party communication. The multi-party computations can include a Fourier series approximation of a continuous function or an approximation of a continuous function using trigonometric polynomials, for example, in training a machine learning classifier using secret shared input data.

Abstract: A method for performing privacy-preserving or secure multi-party computations enables multiple parties to collaborate to produce a shared result while preserving the privacy of input data contributed by individual parties. The method can produce a result with a specified high degree of precision or accuracy in relation to an exactly accurate plaintext (non-privacy-preserving) computation of the result, without unduly burdensome amounts of inter-party communication. The multi-party computations can include a Fourier series approximation of a continuous function or an approximation of a continuous function using trigonometric polynomials, for example, in training a machine learning classifier using secret shared input data.