Abstract: The fast discrete Fourier attack on stream cipher is not suitable for practical application as it requires the pseudorandom sequence to be successive and its complexity grows with the degree of the finite field where the discrete Fourier transform is done. The Fourier attack proposed in this paper is an improvement on the fast discrete Fourier attack. It relaxes the conditions of the former and replaces solving equations in the finite field of some high degree with shifting and adding sequences. The improved Fourier attack is tested on the Bluetooth encryption algorithm E0 to validate its effectiveness.

Key words: Bluetooth encryption E0, fast discrete Fourier attack, stream ciphers, discrete Fourier transform