diff --git a/src/shamira/core.py b/src/shamira/core.py
--- a/src/shamira/core.py
+++ b/src/shamira/core.py
@@ -43,11 +43,13 @@ def reconstruct_raw(*shares):
 	if len({x for (x, _) in shares}) < len(shares):
 		raise MalformedShare("Found a non-unique share. Please check your inputs.")
 
-	secret_len = len(shares[0][1])
+	(xs, payloads) = zip(*shares)
+	secret_len = len(payloads[0])
 	res = [None]*secret_len
+	weights = gf256.compute_weights(xs)
 	for i in range(secret_len):
-		points = [(x, s[i]) for (x, s) in shares]
-		res[i] = (gf256.get_constant_coef(*points))
+		ys = [s[i] for s in payloads]
+		res[i] = (gf256.get_constant_coef(weights, ys))
 	return bytes(res)