Apparatus and system for zero-knowledge proof performed in multi-party computation

An apparatus in a plurality of apparatuses participating in multi-party computation, the apparatus implementing a protocol to perform zero-knowledge proof in secret-distribution-based multi-party computation, the apparatus comprising:

• one or more processors;
• and
• a memory storing instructions which, when the instructions are executed by the one or more processors, cause the apparatus to:
• acquire a share of data related to a matter to be certified, wherein the share is a piece of the data related to the matter to be certified distributed using a secret distribution method;
• output an output share (τi) of evidence (τ) obtained as a result of performing calculation of proposition function by the multi-party computation using the acquired share as an input so that reconstruction is performed to obtain the evidence
• (τ) using the output shares of the evidence collected from the plurality of apparatuses participating in the multi-party computation;
• and
• output an output share (πi) of a proof (π) obtained as a result of performing calculation according to the protocol using the acquired share as an input in a case where a proof by the zero-knowledge proof is requested from a verifier terminal in addition to the output share of the evidence (π),
• wherein verification in the zero-knowledge proof is performed by performing reconstruction to obtain the proof (π) using the output shares of the proof collected from the plurality of apparatuses participating in the multi-party computation,
• wherein the instructions further causes the one or more processors to verify original data of the share has not been falsified, using a digital signature associated with the acquired share.