Privacy Properties and Limitations

# Chain-analysis firms cluster addresses with these heuristics:

# 1. Common-input ownership heuristic (CIOH):
#    If two addresses appear as inputs in the same tx, they're likely owned
#    by the same wallet (because spending requires the corresponding private key).

# 2. Change-output heuristic:
#    Identify which output is change vs payment.
#    Often the change output is the "round number off" one, e.g., 0.5 BTC payment + 0.32847291 change.

# 3. Reuse heuristic:
#    Reused addresses are bound to a single owner over time.

# Counter-strategies:
# - CoinJoin: many users combine inputs in one tx, breaking CIOH
# - Avoid address reuse: each receive uses a new address (BIP-32 HD wallets)
# - Lightning: tx is off-chain; only open/close hits the chain
# - Silent payments (BIP-352): static reusable address; receiver-derived per-tx address

# Example clustering pseudocode:
clusters = {}  # addr -> cluster_id
next_cluster_id = 0

def add_tx(tx):
    global next_cluster_id
    if len(tx.inputs) > 1:
        in_addrs = [tx.input_addr(i) for i in tx.inputs]
        # Find existing cluster for any input addr, or create new
        existing = next((clusters.get(a) for a in in_addrs if a in clusters), None)
        if existing is None:
            existing = next_cluster_id
            next_cluster_id += 1
        # Merge all input addrs into existing cluster
        for a in in_addrs:
            clusters[a] = existing
    # Heuristic: identify change output (smallest output is often change for round payments)
    # ... etc

# Real implementations: BlockSci, WalletExplorer, Chainalysis Reactor, Elliptic