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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.
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 ...
Example of generating an 8-bit CRC. The generator is a Galois-type shift register with XOR gates placed according to powers (white numbers) of x in the generator polynomial. The message stream may be any length. After it has been shifted through the register, followed by 8 zeroes, the result in the register is the checksum.
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 .
Given a prime number q and prime power q m with positive integers m and d such that d ≤ q m − 1, a primitive narrow-sense BCH code over the finite field (or Galois field) GF(q) with code length n = q m − 1 and distance at least d is constructed by the following method. Let α be a primitive element of GF(q m).
A C version [a] of three xorshift algorithms [1]: 4,5 is given here. The first has one 32-bit word of state, and period 2 32 −1. The second has one 64-bit word of state and period 2 64 −1.
void gmix_column (unsigned char * r) {unsigned char a [4]; unsigned char b [4]; unsigned char c; unsigned char h; /* The array 'a' is simply a copy of the input array 'r' * The array 'b' is each element of the array 'a' multiplied by 2 * in Rijndael's Galois field * a[n] ^ b[n] is element n multiplied by 3 in Rijndael's Galois field */ for (c = 0; c < 4; c ++) {a [c] = r [c]; /* h is set to ...
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.