his report presents a new attack called Decimation Attack of most Stream Ciphers. It exploits the property that multiple clocking (or equivalently d-th decimation) of a LFSR can simulate the behavior of many other LFSRs of possible shorter length. It yields then significant improvements of all the previous known correlation and fast correlation attacks. A new criterion on the length is then defined to resist this new attack. Simulation results and complexity comparison are detailed for ciphertext only attack.