Embedded implementations of cryptographic algorithms require countermeasures against side-channel attacks (SCAs), that exploit physical variables measured during the computation. These countermeasures increase cost, power consumption and latency of the device. One class of countermeasures, hiding, consists of a balanced circuit style, including balancing of the capacitances and delays; it requires full connection to avoid memory effect that is an effect caused by repeatedly recharged energy after being only partially discharged at the internal parasitic capacitance. This paper proposes binary decision diagrams (BDDs) to derive complex pull-down networks that fulfill all these requirements while being compact at the same time; it uses sense amplifier-based logic (SABL) to obtain well-balanced pre-charge circuits. An attack based on mutual information analysis (MIA) is applied to the AES S-boxes implemented in our novel secure logic style. After the evaluation at pre-layout SPICE level, the balanced circuit with BDD leaks less information than comparable logic styles, even though the implementation area is reduced by 40.6%, the power consumption up to 46.1% and the delay by 35.2% compared to the classic SABL approach.