Do poly1305 with absolutely no modulo operators

ChaCha20_Poly1305_64/sim/do_poly_1305.py

@@ -1,5 +1,7 @@
 from typing import List
 
+from modulo_theory import friendly_modular_mult, friendly_modulo
+
 def mask_r(r: int) -> int:
     r_bytes = r.to_bytes(16, "little")
 
@@ -40,7 +42,12 @@ def parallel_poly1305(message: bytes, r: int, s: int, lanes: int):
     r = mask_r(r)
     p = 2**130-5
 
-    r_powers = [r**i % p for i in range(lanes+1)]
+    r_powers = [1, r]
+
+    for l_pow_log2 in range(3):
+        l_pow = 2**l_pow_log2
+        for r_pow in range(1,l_pow+1):
+            r_powers.append(friendly_modular_mult(r_powers[l_pow], r_powers[r_pow]))
     
     acc = [0]*lanes
 
@@ -53,12 +60,13 @@ def parallel_poly1305(message: bytes, r: int, s: int, lanes: int):
             idx = i*lanes + j
             power = min(lanes, len(blocks) - idx)
 
+            # There is a division here but we can get this value somehow else
             byte_length = (lane.bit_length() + 7) // 8
             lane += 1 << (8*byte_length)
 
-            acc[j] = ((acc[j] + lane)*(r_powers[power])) % p
+            acc[j] = friendly_modular_mult(acc[j] + lane, r_powers[power])
 
-    combined_acc = sum(acc) % p
+    combined_acc = friendly_modulo(sum(acc), 0)
     combined_acc += s
 
     return combined_acc & (2**128-1)

ChaCha20_Poly1305_64/sim/modulo_theory.py

@@ -50,6 +50,18 @@ def modulo_theory_full(loops: int):
             print(f"{mod_sum=}")
             print(f"{mod_conventional=}")
 
+def friendly_modular_mult(value_a: int, value_b: int) -> int:
+    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)
+
+    return mod_sum
+
 def friendly_modulo(val: int, shift_amount: int) -> int:
     high_part = val >> (130-shift_amount)
     low_part = (val << shift_amount) & (2**130-1)