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The Cost of Secure Restaking vs. Proof-of-Stake

Akaki Mamageishvili, Benny Sudakov

TL;DR

It is shown that the restaking savings compared to PoS protocols can be very large and can asymptotically grow as a square root of the number of validators.

Abstract

We compare the total capital efficiency of secure restaking and Proof-of-Stake (PoS) protocols. First, we consider the sufficient condition for the restaking graph to be secure. The condition implies that it is always possible to transform such a restaking graph into separate secure PoS protocols. Next, we derive two main results: upper and lower bounds on the required extra stakes to add to the validators of the secure restaking graph to be able to transform it into secure PoS protocols. In particular, we show that the restaking savings compared to PoS protocols can be very large and can asymptotically grow as a square root of the number of validators. We also study a complementary question of aggregating secure PoS protocols into a secure restaking graph and provide lower and upper bounds on the PoS savings.

The Cost of Secure Restaking vs. Proof-of-Stake

TL;DR

It is shown that the restaking savings compared to PoS protocols can be very large and can asymptotically grow as a square root of the number of validators.

Abstract

We compare the total capital efficiency of secure restaking and Proof-of-Stake (PoS) protocols. First, we consider the sufficient condition for the restaking graph to be secure. The condition implies that it is always possible to transform such a restaking graph into separate secure PoS protocols. Next, we derive two main results: upper and lower bounds on the required extra stakes to add to the validators of the secure restaking graph to be able to transform it into secure PoS protocols. In particular, we show that the restaking savings compared to PoS protocols can be very large and can asymptotically grow as a square root of the number of validators. We also study a complementary question of aggregating secure PoS protocols into a secure restaking graph and provide lower and upper bounds on the PoS savings.

Paper Structure

This paper contains 6 sections, 11 theorems, 26 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Notation and Model
  3. Results
  4. Restaking Savings
  5. PoS Savings
  6. Conclusion

Key Result

Proposition 1

When the stake vector $\sigma$ satisfies sufficient_eigenlayer, then $\sigma\in \mathcal{W}(G)$.

Figures (2)

  • Figure 1: Example of a secure restaking graph.
  • Figure 2: Example construction for $m=3$.

Theorems & Definitions (27)

  • Example 1
  • Definition 1
  • Definition 2
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Definition 3
  • Proposition 3
  • proof
  • ...and 17 more