LFSR Calculator
Linear feedback shift register (LFSR)
Client-side computation for analysis, verification, and learning. Do not paste production secrets into untrusted sites; prefer local tooling for key material.
Educational / engineering use. RSA mode uses tiny primes for illustration only—not for real key generation.
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What is LFSR Calculator?
A Linear Feedback Shift Register generates pseudo-random binary sequences by shifting bits and feeding back XOR'd outputs into the register. Used in stream ciphers, CRC generation, and hardware testing.
LFSR Formula
Where c_i are feedback coefficients (0 or 1) and b_n is the output bit at step n.
LFSR Step-by-Step
- Select register size and tap positions.
- Enter initial seed state.
- Compute feedback bit using XOR taps.
- Shift register and insert feedback bit.
- Repeat for required sequence length.
LFSR Worked Example
Step 1: b5 = b4 XOR b3 = 1 XOR 0 = 1
Step 2: b6 = b5 XOR b4 = 1 XOR 1 = 0
Step 3: Continue shifting and feedback.
Output sequence example: 1011 -> 1101 -> 0110 -> 1011 ... (repeating).
Where LFSR Calculator Is Applied
- Stream ciphers (A5/1 in GSM mobile encryption)
- Wi-Fi scrambling (802.11 physical layer)
- CRC generation in Ethernet and USB
- Hardware built-in self-test (BIST) in chips
- Pseudo-random number generation in embedded systems
- Digital TV signal scrambling (DVB standard)
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