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.

翻译：我们比较了安全再质押与权益证明（PoS）协议的总资本效率。首先，我们探讨了再质押图保持安全的充分条件。该条件表明，始终有可能将此类再质押图转化为独立的、安全的PoS协议。接着，我们推导出两个主要结果：为了将安全再质押图转化为安全的PoS协议，需要向验证者额外添加的质押量的上界与下界。特别地，我们证明了与PoS协议相比，再质押可实现的节省非常显著，且可随验证者数量的平方根渐近增长。此外，我们还研究了将多个安全的PoS协议聚合为安全再质押图的互补性问题，并给出了PoS节省量的下界与上界。