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This example uses two Galois LFRSs to produce the output pseudorandom bitstream. The Python code can be used to encrypt and decrypt a file or any bytestream ...
In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function of single bits is exclusive-or (XOR). Thus, an LFSR is most often a shift register whose input bit is driven by the XOR of some bits of the overall shift register value.
The Berlekamp–Massey algorithm is an algorithm that will find the shortest linear-feedback shift register (LFSR) for a given binary output sequence. The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an arbitrary field .
This example will use the connection polynomial x 8 + x 4 + x 3 + x 2 + 1, and an initial register fill of 1 0 1 1 0 1 1 0. Below table lists, for each iteration of the LFSR, its intermediate output before self-shrinking, as well as the final generator output. The tap positions defined by the connection polynomial are marked with blue headings.
Grain updates one bit of LFSR and one bit of NLFSR state for every bit of ciphertext released by a nonlinear filter function. The 80-bit NLFSR is updated with a nonlinear 5-to-1 Boolean function and a 1 bit linear input selected from the LFSR. The nonlinear 5-to-1 function takes as input 5 bits of the NLFSR state.
The most common example is the maximum length sequence generated by a (maximal) linear feedback shift register (LFSR). Other examples are Gold sequences (used in CDMA and GPS), Kasami sequences and JPL sequences, all based on LFSRs.
A set of Gold codes can be generated with the following steps. Pick two maximum length sequences of the same length 2 n − 1 such that their absolute cross-correlation is less than or equal to 2 (n+2)/2, where n is the size of the linear-feedback shift register used to generate the maximum length
The correlations which were exploited in the example attack on the Geffe generator are examples of what are called first order correlations: they are correlations between the value of the generator output and an individual LFSR. It is possible to define higher-order correlations in addition to these.