Cryptographic sortition: a secret, stake-weighted committee (Algorand 2017)

Algorand chooses a small committee each round by lottery: every unit of stake is a ticket, and each user privately evaluates a verifiable random function on the round seed to learn how many of their tickets won. Nobody can target the committee in advance, because members reveal themselves only when they vote.

Seats are proportional to stake, and splitting stake into many accounts earns the same expected seats: there is no Sybil advantage. Committee size varies from round to round around its expected value.

import matplotlib.pyplot as plt
import numpy as np

import blockchainkit as bk

Run 300 rounds

stakes = {"alice": 4000, "bob": 3000, "carol": 2000, "dave": 1000}
total, expected = sum(stakes.values()), 30
seats = {name: [] for name in stakes}
for r in range(300):
    seed = r.to_bytes(4, "big")
    for name, stake in stakes.items():
        seats[name].append(
            bk.consensus.sortition(name.encode(), stake, total, expected, round_seed=seed)
        )
means = {name: np.mean(v) for name, v in seats.items()}
for name, stake in stakes.items():
    assert abs(means[name] - expected * stake / total) < 1.5
committee = np.sum([seats[name] for name in stakes], axis=0)

Splitting stake gains nothing

split = [
    sum(
        bk.consensus.sortition(
            f"dave-{i}".encode(), 100, total, expected, round_seed=r.to_bytes(4, "big")
        )
        for i in range(10)
    )
    for r in range(300)
]
assert abs(np.mean(split) - means["dave"]) < 1.0

fig, (left, right) = plt.subplots(1, 2, figsize=(10, 3.8))
left.bar(stakes.keys(), [means[n] for n in stakes], color="#2563eb", label="mean seats")
left.plot(
    list(stakes),
    [expected * s / total for s in stakes.values()],
    "o",
    color="black",
    label="expected",
)
left.set(ylabel="seats per round", title="Seats follow stake")
left.legend()
right.hist(committee, bins=20, color="#16a34a", edgecolor="white")
right.axvline(expected, color="black", linestyle="--")
right.set(xlabel="committee size", title=f"Committee size around {expected}")
fig.tight_layout()

plt.show()

Exercise

The hash here is computed from a private secret, so others cannot check a user’s claimed seats. What does a verifiable random function add, and why must the round seed itself be unpredictable?