Semi-honest Non-colluding Helper Party Model

• Idea: For helper party, we can use any honest-majority protocol to implement dishonest majority protocol by assigning \(n\) shares to the parties and an additional \(t\) shares to the helper party. If \(t=n-1\), then helper and 1 honest party can work together to get things done. Unstoppable Wallets: Chain-assisted Threshold ECDSA and its Applications. Guy Zyskind, Avishay Yanai, and Alex "Sandy" Pentland. 2023
• Idea: To generate a random share: \(P_{1}\) and \(P_{c}\) together generate shares.
  • \(P_{1}\) sends \((n,t+1)\) shares of a random number to all nodes and additional \(t\) shares to \(P_{c}\)
  • \(P_{c}\) sends \((n,t+1)\) shares of a random number to all nodes.
  • All nodes compute their random share as the sum of these two shares.
  • Repeat with \(t+1\) nodes if we want guaranteed output.