Committee sizes computation (#33)

* Added optimal number of committees and sizes function

* Remove main

* Extract common scope code snippet

* Fmt

carnot/committee_sizes.py

@@ -0,0 +1,53 @@
+import math
+from scipy.stats import binom
+
+
+CARNOT_ADVERSARY_THRESHOLD_PER_COMMITTEE: float = 1/3
+CARNOT_NETWORK_ADVERSARY_THRESHOLD: float = 1 / 4
+
+
+def compute_optimal_number_of_committees_and_committee_size(
+        number_of_nodes: int,
+        failure_threshold: float,
+        adversaries_threshold_per_committee: float,
+        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_committees = 1
+    committee_size = number_of_nodes
+    remainder = 0
+    current_probability = 0.0
+    odd_committee = 0
+    while current_probability < failure_threshold:
+        previous_number_of_committees = number_of_committees
+        previous_committee_size = committee_size
+        previous_remainder = remainder
+        previous_probability = current_probability
+        odd_committee = odd_committee + 1
+        number_of_committees = 2 * odd_committee + 1
+        committee_size = number_of_nodes // number_of_committees
+        remainder = number_of_nodes % number_of_committees
+
+        committee_size_probability = binom.cdf(
+            math.floor(adversaries_threshold_per_committee * committee_size),
+            committee_size,
+            network_adversary_threshold
+        )
+        if 0 < remainder:
+            committee_size_plus_one_probability = binom.cdf(
+                math.floor(adversaries_threshold_per_committee * (committee_size + 1)),
+                committee_size + 1,
+                network_adversary_threshold
+            )
+            current_probability = (
+                    1 - committee_size_probability ** (number_of_committees - remainder)
+                    * committee_size_plus_one_probability ** remainder
+            )
+        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 previous_number_of_committees, previous_committee_size, previous_remainder, previous_probability

requirements.txt

@@ -1 +1,2 @@
-blspy~=1.0.16
+blspy~=1.0.16
+scipy~=1.10.1