Embodiments of the invention provide enhanced security solutions which are enforced through the use of cryptographic techniques. It is suited for, but not limited to, use with blockchain technologies such as the Bitcoin blockchain. 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.
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