An efficient threshold distributed elliptic curve key generation and signature method and system

A thresholded distributed elliptic curve key generation and signing procedure, comprising the following steps: S1, in the absence of a trust center to participate, all n nodes generate their own key pair, ptki, puki, where ptki is a private key and puki is a public key. S2, each node processes its own public-private key pair according to a secret sharing protocol, and completes the conversion from threshold (n, n) to threshold (t, n). S3, after determining the t signing nodes, each node generates a threshold private key (t, t) according to threshold logic and completes a mapping from ptki to ptki', where ptki' is the threshold private key, for by means of a procedure comprising: S31, all n nodes, according to the rules of the elliptic curve, each generate their own key pair, ptki, puki, where ptki is the private key, puki is the public key, and i is the node number; S32, all n nodes broadcast their own public keys puki to other nodes, and after receiving the pukx broadcast by other n-1 nodes, they combine n pukx into a complete public key PUK according to the elliptic curve operation. S33, all n nodes perform (t, n) threshold processing according to a selected secret sharing protocol, map ptki to n ptkij segments, and send ptkij to the corresponding node numbered j; and S34, when a signature is performed, t available nodes recover ptki' using the n ptkij received according to the selected secret sharing protocol recovery procedure; and S4, according to a signature logic, each node uses ptki' to complete a communication and a calculation in the signature protocol, and stores the relevant calculation results, and finally completes the overall signature.