Rate Limit Attack Vectors and Parameter Calibration

Status: Draft Last Updated: 2026-02-04

Executive Summary

This document analyzes two categories of attacks that constrain the choice of Initial Rate Limit (IRL) and Second-Order Rate Limit (SORL) parameters. Both attacks require a compromised executor (relayer key + cBEAM), but differ in profitability and mechanism.

The key insight is that IRL and SORL are not independent choices—they are constrained by a bootstrap target (e.g., reach 100M/day within 30 days). Higher SORL allows lower IRL and vice versa. The optimization finds the combination that minimizes total weighted harm from both attack types.

Adopted parameters (for 100M/day target in 30 days):

• SORL: 25% (see smart-contracts/configurator-unit.md for canonical SORL parameters)
• IRL: $100K

Attack Categories

Type 1: Configuration Theft

Mechanism:

• Attacker onboards a rate limit to an uninitialized or misconfigured vault
• Rate limit accumulates from zero over time
• Attacker waits until just before freeze (maximizing accumulated amount)
• Attacker executes attack that drains 100% of deposited funds

Example: Morpho Vault Donation Attack

T+0:     Attacker onboards IRL to uninitialized Morpho vault
         Rate limit = 0, starts accumulating at slope
T+0→18h: Accumulates at original slope
T+18h:   SORL increase applied (earliest possible given `hop=18h`)
         New max = IRL × (1 + SORL)
         New slope = slope × (1 + SORL)
T+18→24h: Accumulates at new slope
T+24h:   Attacker deposits full accumulated amount
         Manipulates vault exchange rate via donation
         Withdraws, draining entire deposit
         Freeze activates (too late)

Key Properties:

• Attacker profit = 100% of loss (direct theft)
• One-time per misconfigured surface
• Bounded by IRL and SORL accumulation
• Requires minimal attacker capital (just gas)
• Eliminable if slippage limits are set atomically with onboarding

Type 2: Operational Extraction

Mechanism:

• Attacker cycles capital through operational routes that have inherent spread/slippage
• Each cycle causes damage to the system (slippage loss)
• Attacker captures a fraction of this damage as profit (via MEV or shorting)

Example: Uniswap Slippage Grinding

T+0:     Attacker increases rate limit (if `hop` allows), then swaps full rate limit through Uniswap
         System loses ~1% to slippage
         Attacker captures ~10% of loss via sandwich MEV
T+12h:   Rate limit replenishes, attacker repeats
T+18h:   Second SORL increase possible (if `hop=18h`), attacker continues
T+24h:   Freeze activates

Key Properties:

• Attacker profit = ~10% of loss (partial extraction)
• Repeatable while attacker has access
• Scales with achieved rate limit
• Requires attacker capital (for sandwich execution)
• Cannot be eliminated, only constrained

Type 2 Profit Models

MEV Extraction:

• Attacker sandwiches their own transaction
• Captures ~10% of slippage as profit
• Requires capital equal to attack size
• Most common approach

Shorting:

• Attacker opens leveraged short position before attack
• Profits from price decline caused by damage
• Rough model: $100M loss → ~1-2% price impact → ~$1-2M short profit
• Extraction rate: ~1-2% (worse than MEV)
• Less traceable but more uncertain

Conclusion: Rational attacker uses MEV when possible. We model 10% extraction rate.

Model Parameters

Fixed Parameters

Calibrated Multipliers

Theft Multiplier Rationale:

Theft is more harmful than equivalent loss because:

• Attacker profit rate: 100% (Type 1) vs 10% (Type 2)
• Higher profit = stronger attacker incentive
• Theft directly enriches attacker, funding future attacks
• 3× is conservative (profit ratio suggests 10×, adjusted for risk factors)

Surface Ratio Rationale:

Type 2 has more attack surfaces because:

• Type 1 requires misconfigured/initializing vaults (limited)
• Type 2 works on any operational route (many)
• Estimated 3× more operational surfaces than initialization surfaces

Damage Rate Assumption

Fixed at 1% for this model.

The 100M/day target represents major, liquid routes (deep Uniswap pools, primary DEX pairs). These high-volume routes naturally have low slippage (~1%).

Higher slippage routes exist but have proportionally lower rate limits:

The N multiplier implicitly captures aggregate exposure across routes of varying slippage/size.

The IRL-SORL Constraint

IRL and SORL are linked by the peacetime bootstrap requirement (one SORL step per day):

IRL × (1 + SORL)^30 = 100M

Solving for IRL:

IRL = 100M / (1 + SORL)^30

The tradeoff:

• Higher SORL → Lower IRL → Less Type 1 exposure
• Higher SORL → More marginal headroom per TTF → More Type 2 marginal exposure

Harm Model

What We're Optimizing

Not optimizing: Base exposure at steady state (100M/day exists regardless of IRL/SORL choice)

Optimizing:

• Type 1: Full IRL exposure (initialization theft)
• Type 2: Marginal SORL exposure (additional damage from SORL increase within TTF)

Type 1 Harm Formula

Type 1 Harm = IRL × Accumulation × Theft_Multiplier × N₁

Where:

• Accumulation = (1 + 0.25 × SORL) — accounts for partial SORL increase in 24h
• Theft_Multiplier = 3
• N₁ = number of Type 1 attack surfaces

Type 2 Marginal Harm Formula

Type 2 Marginal Harm = Base × Headroom × Damage_Rate × Cycles × N₂

Where:

• Base = 100M (target rate limit)
• Headroom = average marginal increase within TTF=24h
  • With hop=18h and attacker increasing at t=0 and t=18h:
    Headroom = 0.75×SORL + 0.25×((1+SORL)^2 - 1) = 1.25×SORL + 0.25×SORL^2
• Damage_Rate = 1%
• Cycles = 2 (per TTF)
• N₂ = 3 × N₁ (surface ratio)

Simplified:

Type 2 Marginal Harm = 100M × (1.25×SORL + 0.25×SORL^2) × 0.02 × 3 × N₁
                     = 6M × (1.25×SORL + 0.25×SORL^2) × N₁

Note: If the attacker cannot use the second bump within TTF (cooldown not available), approximate Headroom ≈ SORL.

Total Harm

Total Harm = Type 1 Harm + Type 2 Marginal Harm
           = N₁ × [3 × IRL × (1 + 0.25×SORL) + 6M × (1.25×SORL + 0.25×SORL^2)]

Critical insight: N₁ factors out completely. The absolute number of attack surfaces doesn't affect the optimal SORL—it only scales total harm proportionally. What matters are the ratios (theft multiplier and surface ratio).

Optimization Results

Minimizing Total Harm per N₁:

Optimal (continuous): SORL ≈ 25.5%, IRL ≈ $109K
Optimal (integer): SORL = 26%, IRL ≈ $97K

At this point, marginal reductions in Type 1 harm (from higher SORL) equal marginal increases in Type 2 harm.

Sensitivity Analysis

Effect of Theft Multiplier

Higher theft multiplier → Higher optimal SORL (prioritize reducing Type 1 by lowering IRL)

Effect of Surface Ratio (R = N₂/N₁)

Higher surface ratio → Lower optimal SORL (prioritize reducing Type 2 marginal)

Effect of Target Rate Limit

Optimal SORL percentage is independent of target scale—only absolute values change.

Attacker Capital Requirements

Type 1 (Configuration Theft):

• Minimal capital required
• Just gas costs to execute transactions
• All profit comes from the misconfigured vault itself
• This makes Type 1 highly attractive (infinite ROI)

Type 2 (Operational Extraction):

• MEV sandwich requires capital ≈ attack size
• Shorting requires margin capital (~10% of position at 10× leverage)
• Limits who can execute large-scale Type 2 attacks
• Provides natural friction against Type 2

Implication: Type 1's low capital requirement is another reason to weight it more heavily in the harm model (captured in the 3× theft multiplier).

Recommendations

Adopted Parameters

Bootstrap Timeline at Adopted Parameters

Note: With IRL=$100K and SORL=25%, the exact 100M target is reached in ~31 days rather than 30.

Operational Risk Capital Requirement

Guardian should hold operational risk capital covering worst-case loss:

ORC ≥ Type 1 Max Loss × N₁
    = $100K × 1.0625 × 10
    = ~$1.06M per executor (for N₁ = 10)

Mitigations Beyond Parameters

Priority mitigation: Make slippage limit configuration atomic with vault onboarding. This eliminates Type 1 entirely, allowing the model to optimize purely for Type 2 (which would suggest lower SORL, higher IRL under the same bootstrap constraint).

Summary

Key Formula:

Total Harm = N₁ × [3 × IRL × (1 + 0.25×SORL) + 6M × (1.25×SORL + 0.25×SORL^2)]

Subject to: IRL × (1 + SORL)^30 = Target

Adopted Parameters (100M/day target):

• SORL = 25%
• IRL = $100K
• Total Harm ≈ $2.36M per N₁

Appendix: Derivation of Accumulation Factor

With rate limit starting at 0 and slope = IRL / 24h:

T = 0 to 18h: Accumulates at original slope
  Accumulated = IRL × (18/24) = 0.75 × IRL

T = 18h: SORL applied
  New slope = slope × (1 + SORL)

T = 18h to 24h: Accumulates at new slope
  Additional = IRL × (1 + SORL) × (6/24) = 0.25 × IRL × (1 + SORL)

Total at T = 24h:
  = 0.75 × IRL + 0.25 × IRL × (1 + SORL)
  = IRL × (0.75 + 0.25 + 0.25 × SORL)
  = IRL × (1 + 0.25 × SORL)

For SORL = 25%: Accumulation factor = 1.0625

Document Version: 0.1