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Merge pull request #35 from logos-co/committee-sizes-AM

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Added description  and reviewed  comm. sizes  algorithm
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Alexander Mozeika 2023-06-27 18:29:22 +01:00 committed by GitHub
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carnot/committee_sizes.py
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@ -1,3 +1,13 @@
"""
This algorithm given the number_of_nodes in the network, fraction of Byzantine nodes in the network, network_adversary_threshold,
fraction of Byzantine modes in a committee, adversaries_threshold_per_committee, and the probability of failure_threshold which can be tolerated computes the maximum number_of_committees and committee_size.
The algorithm computes the current_probability for the number_of_nodes=committee_size*number_of_committees+remainder nodes where the committee_size and committee_size+1 number of nodes are assigned, respectively, to the number_of_committees-remainder and remainder number of committees.
Initially, all number_of_nodes are in one committee, and in subsequent iterations, the number_of_committees is increased by two until the current_probability <= failure_threshold. When the latter condition is violated then the algorithm stops and outputs the number_of_committees, committee_size, remainder and current_probability.
A more detailed description of the algorithm, and of its mathematical aspects, is provided in the "Carnot paper" available at https://www.notion.so/Nomos-Specification-419bfb7a939648e9b3894a90d188c3be?pvs=4
"""
import math
from scipy.stats import binom
@ -13,9 +23,12 @@ def compute_optimal_number_of_committees_and_committee_size(
network_adversary_threshold: float
):
assert failure_threshold > 0
# N is the number of nodes, delta is the failure prob. which can be tolerated,
# A is the fraction of a committee (typical value is 1/3) and P
# is the fraction of adversarial nodes (typical value is 1/4).
# number_of_nodes is the number of nodes in the network
# failure_threshold is the prob. of failure which can be tolerated
# adversaries_threshold_per_committee is the fraction of Byzantine modes in a committee
# network_adversary_threshold is the fraction of Byzantine nodes in the network
number_of_committees = 1
committee_size = number_of_nodes
remainder = 0
@ -48,6 +61,8 @@ def compute_optimal_number_of_committees_and_committee_size(
)
else:
current_probability = 1 - committee_size_probability ** number_of_committees
# return number of committees, K_1, committee size, n_1, number of committees
# with size n_1+1, r_1 and prob. of failure, Prob_1.
# return the number_of_committees, committee_size, remainder and current_probability
# computed at the previous iteration.
return previous_number_of_committees, previous_committee_size, previous_remainder, previous_probability