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Feedback Shift Register (FSR) based stream ciphers are one of the most promising new groups of cryptographic algorithms, which target applications characterized by strong power, area and cost constraints. Due to high sensibility against power analysis attacks, there is a strong need for countermeasures which increase the immunity of this class of ciphers without introducing large power and area overheads. In this paper we study analog multi-level countermeasures which can protect FSR-based stream ciphers against Differential Power Analysis (DPA) attacks, with lower power overhead compared to alternative solutions that can be found in literature. We highlight a trade-off between power consumption and security, and propose an approach which ensures at the same time low power overhead and high security against power analysis attacks.