Methods and devices for generating an
elliptic curve digital signature algorithm signature (r, w) are described. In one embodiment, a method includes: i) forming, by a node, a signing group with other nodes; ii) obtaining, by the node, based on a secure random number: a) a multiplicative inverse of the secure random number; and b) the first signature component, r, wherein the first signature component is determined based on the secure random number and an elliptic curve generator point; iii) determining, by the node, a partial signature based on a private
secret share, the multiplicative inverse of the secure random number and the first signature component; iv) receiving, by the node, partial signatures from other nodes of the signing group; and v) generating, by the node, the second signature component, w, based on determined and received partial signatures.