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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.
Others have mentioned this, but to summarize: the Galois and Fibonacci LFSR should have the numbering of their taps reversed. Specifications like USB define Galois polynomials e.g. x^16 + x^5 + x^4 + x^3 + 1 which corresponds to taps at 16, 5, 4, 3. However, for industry, this is defined for a Galois LFSR with numbering starting from the left.
In their paper, [1] Meier and Steffelbach prove that a LFSR-based self-shrinking generator with a connection polynomial of length L results in an output sequence period of at least 2 L/2, and a linear complexity of at least 2 L/2-1. Furthermore, they show that any self-shrinking generator can be represented as a shrinking-generator.
It is a very fast sub-type of LFSR generators. Marsaglia also suggested as an improvement the xorwow generator, in which the output of a xorshift generator is added with a Weyl sequence. The xorwow generator is the default generator in the CURAND library of the nVidia CUDA application programming interface for graphics processing units.
In cryptography, the shrinking generator is a form of pseudorandom number generator intended to be used in a stream cipher.It was published in Crypto 1993 by Don Coppersmith, Hugo Krawczyk and Yishay Mansour.
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 .
A shop-replaceable unit (SRU) or shop-replaceable component (SRC) is a modular component of an airplane, ship or spacecraft that is designed to be replaced by a technician at a backshop.
Évariste Galois (/ ɡ æ l ˈ w ɑː /; [1] French: [evaʁist ɡalwa]; 25 October 1811 – 31 May 1832) was a French mathematician and political activist. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem that had been open for 350 years.
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