Update arithmetic_circuits.py

Python/arithmetic_circuits.py

@@ -1,19 +1,24 @@
 """
-Demonstrate some ZKP examples in Python
+This Python code demonstrate the examples discussed in the following article by Rareskills:
+    How arithmetic circuits are used to verify zero knowledge proofs
+            https://www.rareskills.io/post/zk-circuits
+
 """
 
+from py_ecc.bn128 import curve_order
+
 # 1. Prove b is the inverse of a
 # The order of the base field of the BN254 curve
-base_field = 21888242871839275222246405745257275088548364400416034343698204186575808495617
+p = curve_order
 def compute_inverse(a):
-    return pow(a, -1, base_field)
+    return pow(a, -1, p)
 
 # Prover --> compute the inverse of a, then give it to the verifier
 a = 15
 b = compute_inverse(a)
 
-# Verifier --> just verify, won't carry out computation
-assert (a*b) % base_field == 1, "Given number is not an inverse of a"
+# Verifier --> just verify, won't carry out any inversion
+assert (a*b) % p == 1, "Given number b is not an inverse of a"
 
 # 2. Prove x is the solution of a polynomial
 def polyeval(x, a, b, c):
@@ -24,10 +29,9 @@ def polyeval(x, a, b, c):
 a = 2
 b = -23
 c = 11
-s = polyeval(x, a, b, c)
 
-# Verifier  --> just verify, won't carry out computation
-assert s == 0, "Given x is not a solution of the polynomial"
+# Verifier  --> just verify if x is the solution, don't  carry out any computations how to find x
+assert 0 == polyeval(x, a, b, c), "Given x is not a solution of the polynomial"
 
 # 3. Proving x is the maximum element in a list of elements
 def maxList(lst):
@@ -38,11 +42,10 @@ def maxList(lst):
 m = maxList(lst)
 x = 11
 
-# Verifier --> just verify, won't carry out computation
+# Verifier --> just verify, don't execute any computations how to find the max value
 assert x == m, "Given input is not the maximum of the list"
 
 # 4. Prove if the given list was sorted
-
 # Prover --> sort the list then give it to the verifier
 lst = [1, 2, 3, 4, 5, 6]
 sortedList = sorted(lst)
@@ -51,7 +54,6 @@ def maxList(lst):
 assert lst == sortedList, "List is not sorted"
 
 # 5. Prove if the list has no duplicates
-
 # Prover --> convert the list to a set, then compare their size
 s = set(lst)