The Ghost Protocol · Heaviest Subtree · Cryptography & Zero-Knowledge Lesson 28

Longest-chain wastes every block on a "stale" sibling. GHOST (Greedy Heaviest Observed SubTree) reuses that work: at each fork, pick the child whose subtree contains the most cumulative work, not the longest single chain. Pre-Merge Ethereum used a GHOST variant that even rewarded uncles, redistributing some of the reward to stale siblings to keep small miners viable.

The trade-off is more bookkeeping for the fork-choice rule — you have to know the subtree weight of every candidate — but the payoff is less wasted work at high block rates. The demo builds a tree where the longest single chain points one way (depth 3) while the heaviest subtree points the other (4 leaves), and shows the two rules diverge on the same data.

The Collision attacks — common mistakes

Confusing GHOST with longest-chain — they pick different heads on the same tree

Recounting the same descendant multiple times in weight

Forgetting that GHOST still requires consensus on which uncles exist

Assuming GHOST eliminates reorgs — it just reduces wasted work

Boss battleBuild a small block tree where longest-chain picks one head but GHOST picks another.

Example code

<!doctype html><html><head><meta charset="utf-8"></head> <body style="background:#06040d;color:#e6e0ff;font-family:monospace;padding:20px"><pre id="o"></pre> <script> // GHOST vs longest-chain on the same tree. const tree = { A:['B','C'], B:['D'], D:['H'], H:[], C:['E','F','G'], E:[], F:[], G:[] }; const subtreeW = (n)=> 1 + tree[n].reduce((s,c)=> s + subtreeW(c), 0); const depth = (n)=> tree[n].length === 0 ? 0 : 1 + Math.max(...tree[n].map(depth)); function walk(start, score){ const path = [start]; while(tree[path[path.length-1]].length){ const cur = path[path.length-1]; let best = tree[cur][0]; for(const c of tree[cur]) if(score(c) > score(best)) best = c; path.push(best); } return path; } const ghostPath = walk('A', subtreeW); const longestP = walk('A', depth); document.getElementById('o').textContent = [ 'subtree weights: A=' + subtreeW('A') + ' B=' + subtreeW('B') + ' C=' + subtreeW('C') + ' D=' + subtreeW('D'), 'longest-chain head: ' + longestP.join(' → ') + ' (depth ' + (longestP.length-1) + ')', 'GHOST head: ' + ghostPath.join(' → '), 'GHOST picks C (subtree=4) over B (subtree=3); longest-chain picks the depth-3 branch B→D→H' ].join('\n'); </script></body></html>

▶ Open the interactive comic issue

the ghost protocol · heaviest subtree

Power-ups you unlock

The Collision attacks — common mistakes

Example code