The basis of every LFSR is developed with a polynomial, which can be irreducible or primitive (Angheloiu et al., 1986 Schneier, 1996). For each clock pulse the new bit in the string is produced using the XOR of certain positions. A string of memory cells that stored a string of bits and a clock pulse can advance the bits with one position in that string. The LFSR (Linear Feedback Shift Register) is the basis of the stream ciphers and it is the most often used one in hardware designs. Many different implementation forms were developed along the years. It was a five-stage device built of vacuum tubes and thyratrons. Introduction A code-breaking machine appeared as one of the first forms of shift register early in the 40's, in Colossus. The analysis of functioning for Primitive Polynomials of 16th degree shows that almost all the obtained results are in the same time distribution. Storing data in Galois Fields allows effective and manageable manipulation, mainly in computer cryptographic applications. Usually LFSR functions in a Galois Field GF(2 n), meaning that all the operations are done with arithmetic modulo n degree Irreducible and especially Primitive Polynomials. Almost all of the major applications in the specific Fields of Communication used a well-known device called Linear Feedback Shift Register.
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