A computer-implemented method comprising: creating at least one proof transaction for recording on a blockchain maintained by a blockchain network , wherein the at least one proof transaction comprises at least an s-part for an Elliptic Curve Digital Signature Algorithm, ECDSA, signature, the s-part having been computed from a set of signature components, each of the signature components having been provided by a participant of a signing subset of a set of keyshare participants; wherein each of the keyshare participants holds an ephemeral keyshare of an unknown ephemeral key, and each of the signing components has been provided by the participant of the signing subset based on the ephemeral keyshare held by that participant; wherein the at least one proof transaction indicates an r-challenge of at least one challenge transaction , so as to cause a node of the blockchain network , in response to receiving the at least one proof transaction , to apply signature verification to: (i) the s-part of the at least one proof transaction , and (ii) one of: (iia) an r-part of the r-challenge , whereby the signature verification fails if the r-part of the r-challenge does not correspond to the unknown ephemeral key, and (iib) an r-part of the at least one proof transaction , and in that event the node is further caused to check that the r-part of the at least one proof transaction satisfies the r-challenge , whereby the signature verification fails if the r-part of the at least one proof transaction does not correspond to the unknown ephemeral key, and the check fails if the r-part of the at least one proof transaction does not satisfy the r-challenge . creating at least one proof transaction for recording on a blockchain maintained by a blockchain network , wherein the at least one proof transaction comprises at least an s-part for an Elliptic Curve Digital Signature Algorithm, ECDSA, signature, the s-part having been computed from a set of signature components, each of the signature components having been provided by a participant of a signing subset of a set of keyshare participants; wherein each of the keyshare participants holds an ephemeral keyshare of an unknown ephemeral key, and each of the signing components has been provided by the participant of the signing subset based on the ephemeral keyshare held by that participant; wherein the at least one proof transaction indicates an r-challenge of at least one challenge transaction , so as to cause a node of the blockchain network , in response to receiving the at least one proof transaction , to apply signature verification to: (i) the s-part of the at least one proof transaction , and (ii) one of: (iia) an r-part of the r-challenge , whereby the signature verification fails if the r-part of the r-challenge does not correspond to the unknown ephemeral key, and (iib) an r-part of the at least one proof transaction , and in that event the node is further caused to check that the r-part of the at least one proof transaction satisfies the r-challenge , whereby the signature verification fails if the r-part of the at least one proof transaction does not correspond to the unknown ephemeral key, and the check fails if the r-part of the at least one proof transaction does not satisfy the r-challenge . (iia) an r-part of the r-challenge , whereby the signature verification fails if the r-part of the r-challenge does not correspond to the unknown ephemeral key, and (iib) an r-part of the at least one proof transaction , and in that event the node is further caused to check that the r-part of the at least one proof transaction satisfies the r-challenge , whereby the signature verification fails if the r-part of the at least one proof transaction does not correspond to the unknown ephemeral key, and the check fails if the r-part of the at least one proof transaction does not satisfy the r-challenge . <EOS>