1. What is an LFSR?

A Linear Feedback Shift Register (LFSR) is a shift register whose input bit is a linear function of its previous state. They are widely used in digital communications and cryptography for generating pseudo-random numbers.

2. How Does the LFSR Work?

The calculator uses the LFSR formula:

Where:

• \( state \) — Current state of the register
• \( tap \) — Tap positions (feedback polynomial)
• \( mask \) — Bitmask defining register length
• \( lsb \) — Least significant bit of current state
• \( \gg \) — Bitwise right shift
• \( \oplus \) — Bitwise XOR operation
• \( \& \) — Bitwise AND operation

Explanation: The register shifts right by one bit. If the lsb was 1, the tap sequence is XOR'd with the new value. The mask ensures proper register length.

3. Importance of LFSRs

Details: LFSRs are efficient in hardware, produce long pseudo-random sequences, and are used in CRC checksums, scrambling, cryptography, and test pattern generation.

4. Using the Calculator

Tips: Enter initial state, tap positions, bitmask, and number of iterations. Common 8-bit tap value is 0xB4 (180), with mask 0xFF (255).

5. Frequently Asked Questions (FAQ)

Q1: What makes a good tap sequence?
A: Taps should correspond to a primitive polynomial to achieve maximum-length sequence (2^n - 1 states for n-bit register).

Q2: How do I choose the mask value?
A: The mask should have bits set for all positions you want in your register (e.g., 0xFF for 8 bits, 0xFFFF for 16 bits).

Q3: What's the significance of the initial state?
A: The initial state (seed) must be non-zero. All-zero state will remain zero. Different seeds produce different sequences.

Q4: Can LFSRs be cryptographically secure?
A: Simple LFSRs are not secure alone, but can be combined to create more secure systems (e.g., A5/1 cipher in GSM).

Q5: What are common applications?
A: Digital broadcasting, GPS, hardware testing, pseudo-random number generation, and stream ciphers.