byzantine stake

Using fresh data for $stake_{global}$ ≈ 0.00M SOL and SOL/USD = , updates every 15min.

Motivated by my participation in Turbin3 Q3 Research Cohort, and inspired by Chorus One's Alpenglow research report section 2.1.

TL;DR

Despite $5f+1$ being 50% cheaper to attack than $3f+1$ and 75% cheaper than $2f+1$ : it's still unprofitable.

Assumptions

Attacker has no SOL, buys at market price, doesn't take SOL from $stake_{global}$, and can add $stake_{byzantine}$ to $stake_{global}$ without limitations.

In a real world scenario, an attacker could get better rates with OTC trades; steal SOL from, or collude with part of $stake_{global}$, and will encounter limitations when adding $stake_{byzantine}$ to $stake_{global}$ in large amounts.

$5f+1$

$5f+1$ byzantine fault tolerance (min. 80% correct nodes) means the network can't preserve integrity if :

$stake_{b}$ resolves to $\frac{1}{4} \cdot stake_{g}$ because attacker adds $stake_{b}$ to $stake_{g}$ :

In a $5f+1$ setup with $stake_{g}$ ≈ 0.00M SOL, attacker has to add $stake_{b}$ ≈ 0.00M SOL ($ 0 B) to the network to degrade its integrity or liveliness, resulting in a +25% change to $stake_{global}$.

$3f+1$

$3f+1$ byzantine fault tolerance (min. 66% correct nodes) means the network can't preserve integrity if :

$stake_{b}$ resolves to $\frac{1}{2} \cdot stake_{g}$ because attacker adds $stake_{b}$ to $stake_{g}$ :

In a $3f+1$ setup with $stake_{g}$ ≈ 0.00M SOL, attacker has to add $stake_{b}$ ≈ 0.00M SOL ($ 0 B) to the network to degrade its integrity or liveliness, resulting in a +50% change to $stake_{global}$.

$2f+1$

$2f+1$ byzantine fault tolerance (min. 50% correct nodes) means the network can't preserve integrity if :

$stake_{b}$ resolves to $stake_{g}$ because attacker adds $stake_{b}$ to $stake_{g}$ :

In a $2f+1$ setup with $stake_{g}$ ≈ 0.00M SOL, attacker has to add $stake_{b}$ ≈ 0.00M SOL ($ 0 B) to the network to degrade its integrity or liveliness, resulting in a +100% change to $stake_{global}$.

Cost Difference

Comparing $3f+1$ to $5f+1$

Given $3f+1$ attack threshold :

And $5f+1$ attack threshold :

$\Delta = \frac{1}{4}stake_{g}$ between $3f+1$ and $5f+1$ :

Translates into a 50% cost reduction :

Comparing $2f+1$ to $5f+1$

Given $2f+1$ attack threshold:

And $5f+1$ attack threshold:

$\Delta = \frac{3}{4} \cdot stake_{g}$ between $2f+1$ and $5f+1$ :

Translates into a 75% cost reduction :

Analysis

Despite $5f+1$ being 50% cheaper to attack than $3f+1$ and 75% cheaper than $2f+1$ : it's still unprofitable, and a very costly endeavor.

However, a sharp decrease of $stake_{global}$, SOL/USD, or increase of Solana TVL could make it profitable.