Verifiable polynomial function secret sharing

A computing system for polynomial function secret sharing by a dealer, wherein a polynomial function of a function client is shared by the dealer and is verifiable by multiple share parties and the function client generates a signed concatenation of first validation parameters, the computing system comprising:

• one or more hardware processors;
• a communication interface executable by the one or more hardware processors and configured to receive a first addend function and a second addend function, wherein a sum of the first addend function and the second addend function equals the polynomial function and each first validation parameter corresponds to a coefficient of the first addend function and a corresponding coefficient of the second addend function;
• a function share generator executable by the one or more hardware processors and configured to generate a function share for each share party based on a sampling of first random polynomials and second random polynomials;
• and
• a validation parameter generator executable by the one or more hardware processors and configured to generate second validation parameters for each share party based on the function shares, each second validation parameter for each share party corresponding to a coefficient of the first random polynomials or the second random polynomials, wherein the communication interface is further configured to transmit the second validation parameters to the share parties and to transmit each function share to a corresponding share party, wherein each function share is verifiable by the corresponding share party as being a share of the polynomial function received by the dealer from the function client, verification being based on the second validation parameters and the signed concatenation of the first validation parameters.

One or more tangible processor-readable storage media embodied with instructions for executing on one or more processors and circuits of a computing device a process for polynomial function secret sharing by a dealer, wherein a polynomial function of a function client is shared by the dealer and is verifiable by multiple share parties and the function client generates a signed concatenation of first validation parameters, the process comprising:

• receiving, by the dealer, a first addend function and a second addend function, wherein a sum of the first addend function and the second addend function equals the polynomial function and each first validation parameter corresponds to a coefficient of the first addend function and a corresponding coefficient of the second addend function;
• generating, by the dealer, a function share for each share party based on a sampling of first random polynomials and second random polynomials;
• generating, by the dealer, second validation parameters for each share party based on the function shares, each second validation parameter for each share party corresponding to a coefficient of the first random polynomials or the second random polynomials;
• transmitting, by the dealer, the second validation parameters to the share parties;
• and
• transmitting, by the dealer, each function share to a corresponding share party, wherein each function share is verifiable by the corresponding share party as being a share of the polynomial function received by the dealer from the function client, verification being based on the second validation parameters and the signed concatenation of the first validation parameters.