galois.FLFSR.step(steps: int = 1) → FieldArray

Produces the next steps output symbols.

Negative values may be passed which reverses the direction of the shift registers and produces outputs in reverse order.

Parameters
steps: int = 1

The direction and number of output symbols to produce. The default is 1. If negative, the Fibonacci LFSR will step backward.

Returns

An array of output symbols of type field with size abs(steps).

Examples

Step the Fibonacci LFSR one output at a time. Notice the first \(n\) outputs of a Fibonacci LFSR are its state reversed.

In [1]: c = galois.primitive_poly(7, 4)

In [2]: lfsr = galois.FLFSR(c.reverse(), state=[1, 2, 3, 4]); lfsr
Out[2]: <Fibonacci LFSR: f(x) = 5x^4 + 3x^3 + x^2 + 1 over GF(7)>

In [3]: lfsr.state, lfsr.step()
Out[3]: (GF([1, 2, 3, 4], order=7), GF(4, order=7))

In [4]: lfsr.state, lfsr.step()
Out[4]: (GF([4, 1, 2, 3], order=7), GF(3, order=7))

In [5]: lfsr.state, lfsr.step()
Out[5]: (GF([6, 4, 1, 2], order=7), GF(2, order=7))

In [6]: lfsr.state, lfsr.step()
Out[6]: (GF([4, 6, 4, 1], order=7), GF(1, order=7))

In [7]: lfsr.state, lfsr.step()
Out[7]: (GF([5, 4, 6, 4], order=7), GF(4, order=7))

# Ending state
In [8]: lfsr.state
Out[8]: GF([0, 5, 4, 6], order=7)

Step the Fibonacci LFSR 5 steps in one call. This is more efficient than iterating one output at a time. Notice the output and ending state are the same from the Scalar output tab.

In [9]: c = galois.primitive_poly(7, 4)

In [10]: lfsr = galois.FLFSR(c.reverse(), state=[1, 2, 3, 4]); lfsr
Out[10]: <Fibonacci LFSR: f(x) = 5x^4 + 3x^3 + x^2 + 1 over GF(7)>

In [11]: lfsr.state
Out[11]: GF([1, 2, 3, 4], order=7)

In [12]: lfsr.step(5)
Out[12]: GF([4, 3, 2, 1, 4], order=7)

# Ending state
In [13]: lfsr.state
Out[13]: GF([0, 5, 4, 6], order=7)

Step the Fibonacci LFSR 10 steps forward.

In [14]: c = galois.primitive_poly(7, 4)

In [15]: lfsr = galois.FLFSR(c.reverse(), state=[1, 2, 3, 4]); lfsr
Out[15]: <Fibonacci LFSR: f(x) = 5x^4 + 3x^3 + x^2 + 1 over GF(7)>

In [16]: lfsr.state
Out[16]: GF([1, 2, 3, 4], order=7)

In [17]: lfsr.step(10)
Out[17]: GF([4, 3, 2, 1, 4, 6, 4, 5, 0, 2], order=7)

In [18]: lfsr.state
Out[18]: GF([3, 1, 1, 0], order=7)

Step the Fibonacci LFSR 10 steps backward. Notice the output sequence is the reverse of the original sequence. Also notice the ending state is the same as the initial state.

In [19]: lfsr.step(-10)
Out[19]: GF([2, 0, 5, 4, 6, 4, 1, 2, 3, 4], order=7)

In [20]: lfsr.state
Out[20]: GF([1, 2, 3, 4], order=7)
Last update: Aug 27, 2022