SQUASH review

poc/plot_prio3_multiproof_robustness.py

@@ -48,8 +48,9 @@ def sum_vec(field_size, num_proofs, length):
     accepting one report in a batch of NUM_REPORTS. Assuming the asymptotically
     optimal chunk length.
     '''
-    chunk_length = max(1, int(math.sqrt(length)))
-    vdaf = Prio3SumVec.with_params(length, 1, chunk_length)
+    bits = 1
+    chunk_length = max(1, length**(-1/2))
+    vdaf = Prio3SumVec.with_params(length, bits, chunk_length)
     gadget_calls = vdaf.Flp.Valid.GADGET_CALLS[0]
 
     base_flp_soundness = soundness(gadget_calls, 2, field_size)
@@ -58,7 +59,7 @@ def sum_vec(field_size, num_proofs, length):
     # polynomial and evaluates the polynomial at a random point. If a gadget
     # output is non-zero, then the output is non-zero except with this
     # probability. This is bounded by the number of roots of the polynomial.
-    circuit_soundness = length / field_size
+    circuit_soundness = length * bits / field_size
 
     return robustness(
         base_flp_soundness + circuit_soundness,  # ia.cr/2019/188, Theorem 5.3
@@ -71,7 +72,7 @@ def sum_vec(field_size, num_proofs, length):
 
 print(math.log2(sum_vec(Field128.MODULUS, 1, 1000000)))
 
-lengths = range(100, 10**5, 100)
+lengths = range(100, 10**6, 100)
 plt.plot(
     lengths,
     [sum_vec(Field128.MODULUS, 1, length) for length in lengths],