Economic Security of Multiple Shared Security Protocols

TL;DR

We address how AVSs inherit security from multiple heterogeneous SSPs and compare isolated (Model $\mathbb{M}$) versus unified (Model $\mathbb{S}$) restaking architectures using convex optimization and game theory. The analysis yields definitions of weak and strong shared security, derives attack-cost bounds, and characterizes market equilibria, showing that equalizing SSP security is optimal in $\mathbb{M}$ while a unified $\mathbb{S}$ architecture provides tighter, more robust system-wide security; bribery considerations further favor non-fragmented designs. Key results indicate that Model $\mathbb{S}$ offers stronger cryptoeconomic security by aggregating stake and harmonizing slashing, whereas Model $\mathbb{M}$ exhibits a higher risk of weakest-link failures unless stake rebalancing enforces equal SSP exposure. The work informs design choices for restaking ecosystems and motivates incentive-compatible stake rebalancing mechanisms to sustain secure, scalable deployment across diverse SSPs.

Abstract

As restaking protocols gain adoption across blockchain ecosystems, there is a need for Actively Validated Services (AVSs) to span multiple Shared Security Providers (SSPs). This leads to stake fragmentation which introduces new complications where an adversary may compromise an AVS by targeting its weakest SSP. In this paper, we formalize the Multiple SSP Problem and analyze two architectures : an isolated fragmented model called Model $\mathbb{M}$ and a shared unified model called Model $\mathbb{S}$, through a convex optimization and game-theoretic lens. We derive utility bounds, attack cost conditions, and market equilibrium that describes protocol security for both models. Our results show that while Model $\mathbb{M}$ offers deployment flexibility, it inherits lowest-cost attack vulnerabilities, whereas Model $\mathbb{S}$ achieves tighter security guarantees through single validator sets and aggregated slashing logic. We conclude with future directions of work including an incentive-compatible stake rebalancing allocation in restaking ecosystems.

Figures (6)

• Figure 1: Model $\mathbb{M}$ (left) with isolated fragmented restaking primitives while Catalysis Model $\mathbb{S}$ (right) with a single consensus pool with a restaking abstraction layer
• Figure 2: A comparison of minimum cost to attack the AVS in the three models. Cost to attack model $\mathbb{S}$$\geq$ Cost to attack a single SSP $\geq$ Cost to attack model $\mathbb{M}$
• Figure 3: Histogram of validator utility from honest participation ($M(v_i)$) across different models under baseline and high-volatility conditions. Under a SOL volatility shock, Model $\mathbb{M}$ shows a clear shift toward lower security margin, while Model $\mathbb{S}$ and Single SSP remain comparatively resilient. The dashed line indicates the ruin threshold ($M(v_i)<0$).
• Figure 4: side-by-side comparison for validator utility from being honest and utility from attacking
• Figure 5: Model $\mathbb{M}$ has a strictly lower bribery threshold than Model $\mathbb{S}$ and is more susceptible to targeted attacks. Model $\mathbb{M}$ has significantly higher amplification factor but greater cost requirements. Models $\mathbb{S}$ and Single SSP demonstrate greater resistance with negative amplification factors and bribery budgets for positive utility

Theorems & Definitions (21)

• Definition 2.1
• Definition 3.1: Weak Shared Security
• Definition 3.2: Strong Shared Security
• Lemma 1: Validator Security Bound
• Lemma 2
• Corollary 2.1: Security Threshold Tightening
• Remark
• Remark
• Lemma 3: Stochastic Dominance levy1992stochastic and Security Bounds
• Theorem 4: Optimal Allocation Minimizes Minimum Risk