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Abstract In this thesis, we will be concerned with stream ciphers which combine the data to be encrypted and a stream of pseudorandom bits generated by the encryption algorithm. Usually with the exclusive-or XOR operation. The mechanism proposed in this thesis is based on a form of LFSR which takes advantage of the inverse tap available from LFSR implementation, we call this form of LFSR a complex LFSR. This thesis investigates the characteristics of a non-linear random key stream generated by using not only the output of the LFSR but also the inverse taps for each stage. A new form of the LFSR generator was built up of one register to meet a primitive stream cipher construction which is fast, easy to use correctly, well understood, and secure. The use of complex LFSR in keystream generators appears to perform well in all NIST statistical tests suite and be a good way of achieving sequences statistical the Golomb`s criteria. We look at a5 keystream generator, which are built up from three registers, and by using the complex LFSR concept and the same feedback functions, to produce many more sequences with the same desirable properties as those produced by the original generator. We established some general properties of the sub-keys output sequences fromm the generalized version of C-LFSR generator algorithm, and investigate these properties further when the registers that make up these generators m-sequences, or de buijn sequences, or a combination of an m-sequence and a de bruijn sequence. We introduce a new concept to encrypt E1 by using a generator 32sub-key that is built up of one single linear feedback shift register 128bits and some logic gates to encrypt E1 module and compare it with the standard of the traditional E1 encryption AES. |