Secure dynamic threshold signature scheme employing trusted hardware

A computer-implemented security method comprising the step of:

• generating an elliptic curve digital signature algorithm signature comprising a first signature component, r, and a second signature component, w, the generation step comprising:
• forming, by a node, a signing group with other nodes;
• 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;
• 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, wherein the partial signature, vi, is determined as:
• v
• i
• =
• k
• -
• 1
• ⁢
• rb
• i
• ⁢
• s
• i
• ⁢
• mod
• ⁢
• p
• ,
• where b;
• is a Lagrangian interpolation coefficient, k−1 is the multiplicative inverse of the secure random number, si is the secret share, r is the first signature component, and p is an order;
• receiving, by the node, partial signatures from other nodes of the signing group;
• and
• generating, by the node, the second signature component, w, based on determined and received partial signatures.