diff --git a/src/shamira/core.py b/src/shamira/core.py
--- a/src/shamira/core.py
+++ b/src/shamira/core.py
@@ -19,7 +19,7 @@ def _share_byte(secret_b, k, n):
 	if not k<=n<255:
 		raise InvalidParams("Failed k<=n<255, k={0}, n={1}".format(k, n))
 	# we might be concerned with zero coefficients degenerating our polynomial, but there's no reason - we still need k shares to determine it is the case
-	coefs = [int(secret_b)]+[int(b) for b in os.urandom(k-1)]
+	coefs = [int(b) for b in os.urandom(k-1)]+[int(secret_b)]
 	points = [gf256.evaluate(coefs, i) for i in range(1, n+1)]
 	return points