Identity Proofs as Node Attributes

Examples of identity proofs include:

• World ID
• zkPassport
• Opacity Network, or other zkTLS authentication with a relevant Web2 provider

These proofs increase a node’s trustworthiness, leading to higher block rewards. This enhances Sybil resistance by providing incentives for genuine users to invest in their EC by submitting proof of their realness.

These proofs can be assigned a score that unlocks a larger block rewards for both this node and any transacting counterparties. Specifically, we boost nodes that have evidence of realness because it provides the network with stronger sybil resistance.

Incorporating Identity Proofs into Eigenvector Centrality#

We represent the network as a bipartite graph $G = (U, V, E)$, where $U$ and $V$ are disjoint sets of nodes representing producers (sellers) and buyers, respectively, and $E$ is the set of edges representing transactions between them.

The eigenvector centrality (EC) $x$ of the nodes in the graph is calculated by solving the eigenvalue problem:

$$\lambda_{\text{max}} \mathbf{x} = \mathbf{A} \mathbf{x},$$

where $A$ is the adjacency matrix of the graph, and $\lambda_{\ ext{max}}$ is the largest eigenvalue.

When a user provides an identity proof, we model this as adding a doping vector $b$ to the eigenvalue equation This can be captured by modifying the EC formula to become an inhomogeneous eigenvalue problem. Suppose user $u$ submits an identity proof that translates into a boost of $b$ in eigenvector centrality. We then define a "doping vector" $\ec{b}_u = (0,0,\dots,0,b,0,\dots,0)$, where the nonzero element $b$ appears in the $u$-th position. The inhomogeneous eigenvalue problem to solve is then:

$$x = \frac{1}{\lambda_{\rm max}} Ax + \vec{b}$$

Technical Impact#

• EC Boost Propagation: The boost in eigenvector centrality resulting from an identity proof propagates through the graph, increasing the centrality of neighboring nodes.
• Higher Rewards: Nodes with verified identity proofs earn greater rewards due to their enhanced EC, making them more attractive as transaction partners.

Next Steps#

We will now explore Service Proofs, which strengthen the reliability of individual transactions in the network.