add simple zk arithmetization example, will be used for bootle16

scripts/halo/bootle16.py

@@ -0,0 +1,62 @@
+# Notes from paper:
+# "Efficient Zero-Knowledge Arguments for Arithmetic Circuits in the
+#  Discrete Log Setting" by Bootle and others (EUROCRYPT 2016)
+
+from finite_fields import finitefield
+import numpy as np
+
+q = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
+fq = finitefield.IntegersModP(q)
+
+# Number of variables
+m = 16
+# Number of rows for multiplication statements
+n = 2
+
+N = n * m
+
+# Initialize zeroed table
+aux = np.full(m, fq(0))
+
+# From the zk-explainer document, we will represent the function:
+#
+#    def foo(w, a, b):
+#        if w:
+#            return a * b
+#        else:
+#            return a + b
+#
+# Which can be translated mathematically to the statements:
+#
+#   ab = m
+#   w(m - a - b) = v - a - b
+#   w^2 = w
+#
+# Where m is an intermediate value.
+
+one = 0
+aux[one] = fq(1)
+
+a = 1
+b = 2
+w = 3
+
+aux[a] = fq(110)
+aux[b] = fq(4)
+aux[w] = fq(1)
+
+# Calculate intermediate advice values
+m = 4
+aux[m] = aux[a] * aux[b]
+
+# Calculate public input values
+v = 5
+aux[v] = aux[w] * (aux[a] * aux[b]) + \
+    (aux[one] - aux[w]) * (aux[a] + aux[b])
+
+# Just a quick enforcement check:
+assert aux[a] * aux[b] == aux[m]
+assert aux[w] * (aux[m] - aux[a] - aux[b]) == aux[v] - aux[a] - aux[b]
+assert aux[w] * aux[w] == aux[w]
+
+# Setup the gates. For each row of a, b and c, the statement a b = c holds