Lightweight authenticated ciphers are specially designed as authenticated encryption (AE) schemes for resource-constrained devices. Permutation-based lightweight authenticated ciphers have gained more attention in recent years. However, almost all of permutation-based lightweight AE schemes only ensure conventional security, i.e., about
c
/
2
-bit security, where
c
is the capacity of the permutation. This may be vulnerable for an insufficiently large capacity. This paper focuses on the stronger security guarantee and the better efficiency optimization of permutation-based lightweight AE schemes. On the basis of APE series (APE,
APE
R
I
,
APE
O
W
, and
APE
C
A
), we propose a new improved permutation-based lightweight online AE mode
APE
+
which supports beyond conventional security and concurrent absorption. Then, we derive a simple security proof and prove that
APE
+
enjoys at most about
min
r
,
c
-bit security, where
r
is the rate of the permutation. Finally, we discuss the properties of
APE
+
on the hardware implementation.