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verify_curves.py

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+import numpy as np
+from sage.all import save, load
+
+def sort_data(security_level):
+    from operator import itemgetter
+
+    # step 1. load the data
+    X = load("{}.sobj".format(security_level))
+
+    # step 2. sort by SD
+    x = sorted(X["{}".format(security_level)], key = itemgetter(2))
+
+    # step3. replace the sorted value
+    X["{}".format(security_level)] = x
+
+    return X
+
+def generate_curve(security_level):
+
+    # step 1. get the data
+    X = sort_data(security_level)
+
+    # step 2. group the n and sigma data into lists
+    N = []
+    SD = []
+    for x in X["{}".format(security_level)]:
+        N.append(x[0])
+        SD.append(x[2] + 0.5)
+    
+    # step 3. perform interpolation and return coefficients
+    (a,b) = np.polyfit(N, SD, 1)
+
+    return a, b
+    
+
+def verify_curve(security_level, a = None, b = None):
+
+    # step 1. get the table and max values of n, sd
+    X = sort_data(security_level)
+    n_max = X["{}".format(security_level)][0][0]
+    sd_max = X["{}".format(security_level)][-1][2]
+
+    # step 2. a function to get model values
+    def f_model(a, b, n):
+        return ceil(a * n + b)
+
+    # step 3. a function to get table values
+    def f_table(table, n):
+        for i in range(len(table)):
+            n_val = table[i][0]
+            if n < n_val:
+                pass
+            else:
+                j = i 
+                break
+        
+        # now j is the correct index, we return the corresponding sd
+        return table[j][2]
+
+    # step 3. for each n, check whether we satisfy the table
+    n_min = max(2 * security_level, 450, X["{}".format(security_level)][-1][0])
+    print(n_min)
+    print(n_max)
+
+    for n in range(n_max, n_min, - 1):
+        model_sd = f_model(a, b, n)
+        table_sd = f_table(X["{}".format(security_level)], n)
+        print(n , table_sd, model_sd, model_sd >= table_sd)
+
+        if table_sd > model_sd:
+            print("MODEL FAILS at n = {}".format(n))
+            return "FAIL"
+
+    return "PASS", n_min
+
+
+def generate_and_verify(security_levels, log_q, name = "verified_curves"):
+
+    data = []
+
+    for sec in security_levels:
+        print("WE GO FOR {}".format(sec))
+        # generate the model for security level sec
+        (a_sec, b_sec) = generate_curve(sec)
+        # verify the model for security level sec
+        res = verify_curve(sec, a_sec, b_sec)
+        # append the information into a list
+        data.append((a_sec, b_sec - log_q, sec, res[0], res[1]))
+        save(data, "{}.sobj".format(name))
+    
+    return data
+
+# To verify the curves we use
+generate_and_verify([80, 96, 112, 128, 144, 160, 176, 192, 256], log_q = 64)
+