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# Questions tagged [lfsr]

Linear Feedback Shift Register, a pseudorandom bit generator which can be efficiently implemented in hardware.

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### Proof of theorem by Lin and Costello

I want to prove the following theorem in LFSR: If $f(x)$ is a polynomial in $\text{GF}(2)$ with exponent $e$, which means $f(x) \mid x^e + 1$. I want to prove that $e \le 2^n -1$. I had some attempts ...
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### Why is firmware implementation not preferred for more lfsr based encryption schemes?

Given that an algorithmic implementation of a linear feedback shift register based encryption scheme is (much?) more secure against side channel attacks; why are hardware platforms usually used? I get ...
181 views

### How to identify if a legacy encryption algorithm used in my programming language is secure?

I used an open-source programming language called Lucee / Cfscript that is closely related to Adobe Coldfusion. The default function that developers use to encrypt and decrypt data (usually for ...
404 views

### Decrypting 3 Binaries | LFSR

I have three binary arrays each one representing the pixels of an image. For example, if the picture size is 100 pixels X 100 pixels. Then the binary array would be 100×100×8×3 bits. These files are ...
112 views

### Finding the polynomial for LFSR given it's length and output

Let's say that i know that the output of an LFSR with length 4 is 1,1,1,0,0,1,1. Constructing the 3 equations modulo 2: $$s_{4} = \sum\limits_{i=1}^{4}c_{i}s_{4-i} \Leftrightarrow c_{2}+c_{3}+c_{4}=0$$...
420 views

### On bent combining functions

Bent functions are Boolean functions with maximum nonlinearity and are widely studied for their potential applications in cryptography. Let's say you want to use a simple $2$-input AND gate as a ...
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### Determining the coefficients of a binary LFSR

I am currently leaning about LFSRs. I was told that a binary LFSR with length m has a form of $s_m=a_0s_0+a_1s_1+\ldots+a_{m-1}s_{m-1}$ are binary numbers. $a_0\ldots a_{m-1}$ are hidden and we are ...
1k views

### Why do Mersenne Twister use Mersenne prime but not regular prime numbers

I'm trying to figure out why Mersenne Twister use exactly Mersenne prime numbers but not regular primes. What makes Mersenne prime numbers more appropriate for this role than regular primes?
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### Distinct sequences in a Fibonacci LFSR

How many distinct sequences can a $128$-bit Fibonacci LFSR (considering $4$ taps set for the maximum period) generate? Will all $2^{128} - 1$ distinct seeds produce distinct sequences? Also, let's say ...
148 views

### Is there a standard for LFSRs to test against for use in a stream cipher?

I am trying to implement a stream cipher that uses an LFSR PRNG. I have found resources online that give good primitive polynomials, but I am struggling to find resources with the initial states as ...
1 vote
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1 vote
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### Can the Berlekamp-Massey algorithm falsely detect an LFSR?

Is it possible that the BMA detects an irreducible polynomial from a sequence that was not generated by an LFSR? I am feeding a sequence into the BMA under the assumption that it was generated by an ...
1k views

### How to clock a linear feedback shift register?

I have some trouble understanding what happens when a LFSR is clocked. I have tried many examples but I do not get the correct result. Can anyone point out my errors? I have the following polynomial: ...
1k views

### Convert m-Sequence into a de Bruijn Sequence

In his paper Alternating Step Generator Controlled by de Bruijn Sequence, C.G. Günther states on page three that a de Bruijn sequence (..) can easily be obtained from an m-sequence (maximal length ...
1 vote
2k views

### Decrypting LFSR, knowing the beginning of the cyphertext, and nothing else

I have a cipher-text in binary, I know the beginning of the plain-text. I know that it is encrypted using LFSR, and I know nothing else. How can I attack, and decrypt it? What I have tried; I ...
2k views

### Attack on LFSR key stream generator

Alright this is a question I found on one of my books: Given is a stream cipher which uses a single LFSR as key stream generator. The LFSR has a degree of 256. How many plaintext/ciphertext bit ...
2k views

### XOR LFSR and all zero state

I read this in a description of Linear Shift Feedback Registers Note that the allzero state must be excluded. If an LFSR assumes this state, it will get “stuck” in it, i.e., it will never be able to ...
104 views

### Finding initial key of Fibonacci LFSR knowing only polynomial and output stream-cipher

I need to know whether it is possible to find the initial key of a Fibonacci LFSR knowing only length and taps and output stream-cipher bit sequence? Plaintext is not ASCII, nor some other sort of ...
1 vote
623 views

### What tools are there to reverse-engineer an LFSR besides the BMA?

I have a certain timecode which I can’t seem to figure out. We gave successfully decoded other codes for the same purpose with the Berlekamp-Massey algorithm, but this code seems to have a linear ...
173 views