Preventing Collusion

Huma Network is built to be resistant to collusion. There are two factors underlying this:

1. Economic security of Ethereum shared with the operators

2. Semi-trusted paranets enabled by linear secret sharing

The economic security provides a disincentive for nodes to be found to have colluded, as long as the benefits of collusion do not exceed the economic risk of being caught colluding. However, for cases when secrets worth more than the economic security level are being shared with Human network, semi-trusted nodes are a helpful addition.

Semi-trusted paranets are parties, or sets of parties, that run independent Human networks. They can be centralized or decentralized. They are trusted to prevent collusion but not have access to any sensitive data. Because of the linear homomorphisms in elliptic curves,

$$bA + sA = (b+s)A$$

i.e. Human Network with secret key b can operate independently from the semi-trusted paranet with secret key s. They both do their scalar multiplications by the input point A. The end user can add their results and get a result as if they came from a single Human Network with secret key b+s. The public key of the joint network would be the sum of public keys from both networks:

$$bG + sG$$