Add modulo theory

ChaCha20_Poly1305_64/sim/modulo_theory.py

@@ -0,0 +1,75 @@
+import random
+
+PRIME = 2**130-5
+
+def modulo_theory_simple(loops: int):
+    prime = 97
+
+    for _ in range(loops):
+        value_a = random.randint(1,97)
+        value_b = random.randint(1,97)
+
+        value_a_high = value_a // 10
+        value_a_low = value_a % 10  # Ignore this modulo, in base 2 it is a mask
+
+        prod_high = value_a_high * value_b
+        prod_low = value_a_low * value_b
+
+        mod_high = (prod_high*10) % prime
+        mod_low = prod_low % prime
+
+        mod_sum = (mod_high + mod_low) % prime
+
+        mod_conventional = (value_a * value_b) % prime
+
+        if mod_sum != mod_conventional:
+            print(f"{value_a}")
+            print(f"{value_b}")
+            print(f"{mod_sum=}")
+            print(f"{mod_conventional=}")
+
+def modulo_theory_full(loops: int):
+    for _ in range(loops):
+        value_a = random.randint(1,PRIME)
+        value_b = random.randint(1,2**128)
+
+        a_partials = [(value_a >> 26*i) & (2**26-1) for i in range(5)]
+
+        prods = [a_partial * value_b for a_partial in a_partials]
+
+        mods = [friendly_modulo(prod, 26*i) for i, prod in enumerate(prods)]
+
+
+        mod_sum = friendly_modulo(sum(mods), 0)
+
+        mod_conventional = (value_a * value_b) % PRIME
+
+        if mod_sum != mod_conventional:
+            print(f"{value_a}")
+            print(f"{value_b}")
+            print(f"{mod_sum=}")
+            print(f"{mod_conventional=}")
+
+def friendly_modulo(val: int, shift_amount: int) -> int:
+    high_part = val >> (130-shift_amount)
+    low_part = (val << shift_amount) & (2**130-1)
+
+    high_part *= 5
+
+    val = high_part + low_part
+
+    high_part = val >> 130
+    low_part = val & (2**130-1)
+
+    high_part *= 5
+
+    val = high_part + low_part
+
+    if val >= PRIME:
+        val -= PRIME
+
+    return val
+
+if __name__ == "__main__":
+    #modulo_theory_simple(10000000)
+    modulo_theory_full(100000)