Attacks on cryptocircuits are becoming increasingly sophisticated, requiring designers to include more and more countermeasures in the design to protect it against malicious attacks. Fault Injection Attacks and Differential Fault Analysis have proven to be very dangerous as they are able to retrieve the secret information contained in cryptocircuits. In this sense, Trivium cipher has been shown to be vulnerable to this type of attack. This paper presents four different fault detection schemes to protect Trivium stream cipher implementations against fault injection attacks and differential fault analysis. These countermeasures are based on the introduction of hardware redundancy and signature analysis to detect fault injections during encryption or decryption operations. This prevents the attacker from having access to the faulty key stream and performing differential fault analysis. In order to verify the correct operation and the effectiveness of the presented schemes, an experimental system of non-invasive active attacks using the clock signal in FPGA has been designed. This system allows to know the fault coverage for both multiple and single faults. In addition, the results of area consumption, frequency degradation, and fault detection latency for FPGA and ASIC implementations are presented. The results show that all proposed countermeasures are able to provide a fault coverage above 79% and one of them reaches a coverage of 99.99%. It has been tested that the number of cycles for fault detection is always lower than the number of cycles needed to apply the differential fault analysis reported in the literature for the Trivium cipher.