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A standard LFSR has a single XOR or XNOR gate, where the input of the gate is connected to several "taps" and the output is connected to the input of the first flip-flop. A MISR has the same structure, but the input to every flip-flop is fed through an XOR/XNOR gate. For example, a 4-bit MISR has a 4-bit parallel output and a 4-bit parallel input.
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 .
At each advance, the bit on the far left (i.e. "data in") is shifted into the first flip-flop's output. The bit on the far right (i.e. "data out") is shifted out and lost. The data is stored after each flip-flop on the "Q" output, so there are four storage "slots" available in this arrangement, hence it is a 4-bit register.
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. The last one has four 32-bit words of state, and period 2 128 −1. The 128-bit algorithm passes the diehard tests.
In the original Grain Version 0.0 submission of Grain, one bit of the 80-bit NLFSR and four bits of the 80-bit LFSR are supplied to a nonlinear 5-to-1 Boolean function (that is chosen to be balanced, correlation immune of the first order and has algebraic degree 3) and the output is linearly combined with 1 bit of the 80-bit NLFSR and released ...
It is known how to generate an n-bit NLFSR of maximal length 2 n, generating a De Bruijn sequence, by extending a maximal-length LFSR with n stages; [2] but the construction of other large NLFSRs with guaranteed long periods remains an open problem. [3]
If you take every sequential group of three bit words in the PRBS3 sequence (wrapping around to the beginning for the last few three-bit words), you will find the following 7 word arrangements: " 101 1100" → 101 "1 011 100" → 011 "10 111 00" → 111 "101 110 0" → 110 "1011 100 " → 100 " 1 0111 00 " → 001 (requires wrap) " 10 1110 0 ...
A straightforward hardware implementation of Trivium would use 3488 logic gates and produce one bit per clock cycle. However, because each state bit is not used for at least 64 rounds, 64 state bits can be generated in parallel at a slightly greater hardware cost of 5504 gates. Different tradeoffs between speed and area are also possible.