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Linear Feedback Shift Register

Tool to use a linear feedback shift register or LFSR and generate pseudo-random bits using XOR exclusive OR operations.

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Linear Feedback Shift Register -

Tag(s) : Informatics

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# Linear Feedback Shift Register

## LFSR Bits Generator

### What is a linear feedback shift register? (Definition)

A linear feedback shift register or LFSR is a system that generates bits from a register and a feedback function.

After several iterations, the register returns to a previous state already known and starts again in a loop, the number of iterations of which is called its period.

In practice, this kind of LFSR register is useful in cryptography because it allows the generation of pseudo-random numbers when the period is long enough.

### How to use a LFSR?

From a current state of the register, a bit selection is chosen to apply an XOR operation to it.

The result is then concatenated at the start of the register (on the left) while the final value (on the right) is deleted from the register and displayed at the output.

Example: The register is 1010, an XOR ⊕ is applied to bits 0 and 2 (numbered from left to right starting from 0)

StepRegisterXOROutput
0_______01010 ⊕ 0 = 0
1______0010_0 ⊕ 1 = 11
2_____1001__1 ⊕ 0 = 10
3____1100___1 ⊕ 0 = 11
4___1110____1 ⊕ 1 = 00
5__0111_____0 ⊕ 1 = 10
6_1011______0 ⊕ 1 = 11
70101_______0 ⊕ 0 = 01

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