Probabilistic Sampling & Light Node Security

LayerEdge introduces a novel probabilistic sampling approach to ensure decentralized and efficient verification at scale. This mechanism is crucial for maintaining the network's trust-minimized security without requiring every node to verify the full proof set. Instead, Light Nodes verify a randomly chosen subset of aggregated proofs, contributing collectively to the overall integrity of the system.

Random Subset Verification

• Every Light Node selects a random subset of the aggregated proof batch for local verification.
• This dramatically reduces the computational burden on individual nodes.
• Even though each node only checks a fraction of the data, the combined network can confidently assess the correctness of the entire batch.

This strategy enables LayerEdge to:

• Scale verifiability linearly with node count
• Avoid centralized or heavyweight verifier bottlenecks
• Maintain decentralization while optimizing performance

Randomness Source Design

To prevent manipulation or bias in subset selection, randomness is derived from:

• Bitcoin Block Headers: Immutable, verifiable, and globally synchronized.
• Verifiable Random Functions (VRFs): Each node uses a unique seed (e.g., nodeSeed) to compute its proof subset in a tamper-resistant manner.

Pseudocode for Subset Selection

function RandomSubsetSelection(nodeSeed, blockHeaderHash):
    combinedRand = Hash(nodeSeed, blockHeaderHash)
    subset = DeterministicSubsetFunction(combinedRand)
    return subset

This design guarantees:

• Unpredictability: Adversaries cannot precompute or game the selection.
• Verifiability: Other participants can validate that a node's subset was selected fairly using its VRF output.

Exponential Fraud Detection

One of the most powerful aspects of probabilistic verification is its statistical strength:

If an adversary inserts a fraudulent proof in a batch of size M, and L Light Nodes independently select subsets to verify, the probability that the fraudulent proof escapes detection is:

$$P(\text{Fraud Undetected}) = \left(1 - \frac{1}{M} \right)^L \approx e^{-L/M}$$

As the number of nodes L grows, this probability drops exponentially, making fraud practically impossible in a well-participated network.

Node Collusion Resistance

LayerEdge's decentralized random verification model is naturally resistant to collusion:

• Even if some Light Nodes collude or skip checks, others (acting independently) still have a high chance of catching invalid proofs.
• Each node's subset selection is verifiable and tamper-resistant.
• Fraud detection and slashing mechanisms discourage collusion by raising the cost of dishonesty.

Economic Enforcement

Security isn't just cryptographic—it's economic:

• Rewards: Light Nodes that honestly verify and report results earn LayerEdge tokens.
• Bounties: Any node that detects fraud and submits a valid Disprove Transaction earns a bonus.
• Slashing: Nodes that approve bad proofs or fail to verify properly are penalized or lose staked tokens.

These incentives ensure rational actors are aligned with the network's security goals.

Mechanism	Benefit
Random Subset Verification	Scalable and efficient zk-proof checking
Bitcoin Header + VRF Randomness	Unpredictable and verifiable selection
Exponential Detection Guarantee	Near-zero chance of undetected fraud in large networks
Collusion Resistance	Independent verification prevents centralized manipulation
Slashing + Bounties	Strong economic disincentives for malicious behavior

LayerEdge's Light Node system is not just efficient—it's one of the most trust-minimized, decentralized zk-verification systems designed to scale zk-proofs on Bitcoin.