Security Analysis

LayerEdge's Light Node verification system is grounded in a probabilistic security model that leverages decentralized sampling, cryptographic randomness, and economic incentives. Despite each Light Node only verifying a subset of zk-proofs, the system achieves extremely high fraud detection guarantees due to random redundancy and economic alignment.

This section explores the mathematical, economic, and structural security assumptions underpinning Light Node operation.

Exponential Fraud Detection Probability

The core idea behind LayerEdge's Light Node security model is that the probability of a fraudulent proof escaping detection declines exponentially as the number of independent verifiers increases.

Formal Model

Let:

• $L$ = Number of Light Nodes
• $M$ = Total number of zk-proofs in the aggregated batch

If each Light Node randomly selects and verifies one proof, the probability that a single fraudulent proof remains undetected is given by:

$$P_{\text{undetected}} = \left(1 - \frac{1}{M}\right)^L \approx e^{-L/M}$$

Interpretation

• The more Light Nodes participate, the lower the probability that a fraudulent proof will escape detection.
• Even with a modest number of Light Nodes (e.g., 50–100), the network achieves strong coverage and high assurance.
• This exponential decay makes LayerEdge's verification highly robust even at large scales.

Example:

If $M=1000$ and $L=500$, the probability of fraud going undetected is:

$$P_{\text{undetected}} = \left(1 - \frac{1}{1000}\right)^{500} \approx 0.6065$$

However, if $L=5000$:

$$P_{\text{undetected}} = \left(1 - \frac{1}{1000}\right)^{5000} \approx 0.0067$$

Just by increasing Light Node participation, LayerEdge radically improves fraud detection reliability.

Economic Disincentives for Malicious Behavior

LayerEdge includes built-in economic punishments to discourage misbehavior.

Penalty Model

Malicious Light Nodes that:

• Fail to verify assigned proofs,
• Submit false attestations, or
• Approve invalid zk-proofs

...are penalized in the following ways:

• Loss of $EDGEN token rewards for that cycle
• Possible slashing of staked assets (if bonded)
• Reputation downgrade within the LayerEdge verifier registry
• Temporary or permanent exclusion from the validator set

Rational Assumption

Rational actors will choose to:

• Verify honestly, since failure leads to penalties
• Actively validate to earn base and bounty rewards

This aligns network health with economic self-interest.

Honest Node Incentivization

Light Nodes that verify correctly and/or detect fraud receive:

• Base verification rewards in $EDGEN
• Bounty rewards for catching invalid zk-proofs
• Enhanced future selection weight in the verifier set

This economic model:

• Encourages proactive behavior
• Rewards fraud detection
• Reinforces decentralized validation at scale

Collusion Resistance

Threat Model

What if malicious nodes collude to ignore a fraudulent proof?

Defense by Design

• Each Light Node independently samples proofs via VRF + Bitcoin block hash.
• The subset of proofs seen by one node is unpredictable to others.
• This ensures that honest nodes will likely be assigned the same proof and can flag it.

Collusion Cost

For collusion to succeed:

• All Light Nodes assigned to the fraudulent proof must be malicious.
• As honest node count increases, the chance of full collusion over any given proof becomes negligible.

LayerEdge's randomized assignment and auditability guarantee that:

• Fraud is visible,
• Honest nodes have the power to dispute,
• Collusion at scale is economically irrational and statistically implausible.

Security Mechanisms

Security Mechanism	Description
Random Sampling	Ensures decentralized, unpredictable proof assignment
Exponential Detection	Fraud detection probability improves with every added node
Merkle Inclusion Proofs	Ensure proofs are part of the committed batch
Economic Penalties	Deter malicious behavior via slashing or exclusion
Bounty Rewards	Motivate honest behavior and fraud reporting
Collusion Resistance	Independent randomness ensures overlapping verification
Auditability	All validation reports and disputes are publicly verifiable

LayerEdge's Light Node architecture achieves scalable and provably secure decentralized verification by combining:

• Mathematical guarantees (via exponential fraud detection),
• Economic design (via token incentives and slashing),
• Cryptographic randomness (via VRFs and block headers).

This design ensures that even in the presence of adversaries or collusion attempts, invalid proofs are highly unlikely to persist, making LayerEdge a robust foundation for global zk-verification.