anonymity_set.py

"""
Given a number of validators, compute the expected number of P2P nodes that correspond to them given the current network configuration
"""

import numpy as np
import random
import sys
from matplotlib import pyplot as plt

def Zipf(a: np.float64, min: np.uint64, max: np.uint64, size=None):
    """
    Generate Zipf-like random variables,
    but in inclusive [min...max] interval

    Taken from: https://stackoverflow.com/a/57420941
    """
    if min == 0:
        raise ZeroDivisionError("")

    v = np.arange(min, max+1) # values to sample
    p = 1.0 / np.power(v, a)  # probabilities
    p /= np.sum(p)            # normalized

    # print("Weight of the first 20%%: %s" % sum(p[:int(max*0.2)]))

    return np.random.choice(v, size=size, replace=True, p=p)

N_RUNS = 1000 # simulation runs

# An alpha parameter for a power law distribution that provides a 80-20 shape
POWER_LAW_ALPHA = 0.97

# Number of P2P nodes on the network
NODES = 5000
# Number of validators on the network
VALIDATORS = 250000
# The anonymity set (in validators)
ANONYMITY_SET = 8192

n_total = 0
for _ in range(N_RUNS):
    # For every validator, assign a unique node ID to it, using a discrete power-law 80-20 distribution
    validators = Zipf(POWER_LAW_ALPHA, 1, NODES, VALIDATORS)

    # Now choose 8192 random validators (i.e. proposers)
    proposers = random.choices(validators, k=ANONYMITY_SET)

    # Count their unique nodes
    n_total += len(set(proposers))

print("Average number of nodes in the anonymity set: %s" % (n_total/N_RUNS))

# Since we are here let's also plot a graph showing nodes (x axis) to validators per node (y axis) for the zipf(alpha)-law used
# plt.hist(validators, bins=5000)
# plt.title("Zipf")
# plt.show()

Graph showing nodes (x axis) to validators per node (y axis) for the zipf(alpha)-law used