add generalized barycentric degree check for degree < 2^l

barycentric_low_degree_check/barycentric_low_degree_check_pow2.py

@@ -0,0 +1,39 @@
+# A generalized low degree check based on Dankrad's check for degree < 2^l
+from random import randint, shuffle, choice
+from poly_utils import PrimeField
+
+MODULUS = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
+PRIMITIVE_ROOT = 7
+
+assert pow(PRIMITIVE_ROOT, (MODULUS - 1) // 2, MODULUS) != 1
+assert pow(PRIMITIVE_ROOT, MODULUS - 1, MODULUS) == 1
+
+primefield = PrimeField(MODULUS)
+
+WIDTH = 32       # number of evaluations at roots of unity
+M = 4            # check degree < M
+N = WIDTH // M   # number of cosets
+
+ROOT_OF_UNITY = pow(PRIMITIVE_ROOT, (MODULUS - 1) // WIDTH, MODULUS)
+DOMAIN = [pow(ROOT_OF_UNITY, i, MODULUS) for i in range(WIDTH)]
+
+def check(f):
+    r = randint(0, MODULUS)
+    rm = pow(r, M, MODULUS)
+    sums = [0] * N
+
+    for i in range(WIDTH):
+        coset_idx = i % N
+        sums[coset_idx] += primefield.div(f[i] * DOMAIN[i], r - DOMAIN[i])
+
+    for i in range(N):
+        sums[i] = primefield.div(primefield.mul(sums[i], rm - DOMAIN[i * M]), DOMAIN[i * M])
+
+    return sums.count(sums[0]) == N
+
+fc = [randint(0, MODULUS) for i in range(M)]
+f = [primefield.eval_poly_at(fc, x) for x in DOMAIN]
+
+assert check(f)
+f[randint(0, len(f) -1)] += 1
+assert not check(f)