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

learn more… | top users | synonyms

6
votes
1answer
300 views

Can a LFSR be cryptographically secure?

I have been looking at an embedded microcontroller which has a cryptographic hardware engine (in particular the PIC32MZ family). These devices have what they advertise as a cryptographically secure ...
5
votes
1answer
138 views

Determine LFSR phase quickly?

I know it's possible with work backwards from the output bits of an LFSR to determine its feedback polynomial in a O(n) fashion. I'm also curious if, given an LFSR state and polynomial, is it ...
4
votes
1answer
258 views

LFSR dynamic mutation

In normal LFSR, the state is a function of the initial seed, taps positions and time, nothing else. I've seen a modification of LFSR that works like this: ...
3
votes
2answers
271 views

Number of states in a LFSR

Do all $2^{\ell}$ (where $\ell$ is the bit length of the shift register) states always occur in a LFSR or can I choose my taps badly so some states are skipped and the period is shortened? If so is ...
3
votes
2answers
977 views

Cryptanalysis of Linear Feedback Shift Registers

It is well known that simple m-sequence linear feedback shift registers have a linear algebraic structure and therefore the generator seed can easily be deduced using the Berlekamp-Massey algorithm. ...
3
votes
1answer
174 views

Maximal-length LFSR with $n$ bits when the factorization of $2^n-1$ is unavailable?

There's a classical method to efficiently test if a LFSR with $n$ bits is maximal-length (or equivalently, if the feedback polynomial is primitive), when the factorization of $2^n-1$ is available. Do ...
3
votes
1answer
200 views

Nonlinearity of the J-K Flip Flop

In Encryption Schemes for Computer Confidentiality, Pless describes how to use the J-K flip flop as a nonlinear combiner for linear feedback shift registers. This generator was broken because the J-K ...
3
votes
1answer
155 views

Convert m-Sequence into a de Bruijn Sequence

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

Combining LFSRs for Stream Ciphers: Why do we need high non-linearity?

Linear Feedback Shift Registers (LFSRs) can be excellent (efficient, fast, and with good statistial properties) pseudo-random generators. Many stream ciphers are based on LFSRs and one of the possible ...
2
votes
2answers
512 views

Berlekamp-Massey algorithm: case when sequence length is less than double the length of the LFSR

Suppose that we have a sequence of $N$ digits which is produced by a Linear Feedback Shift Register (LFSR) and the shortest such LFSR is of length $L$. A very important tool in cryptanalysis of stream ...
2
votes
1answer
237 views

LFSR using words

If I've got an LFSR, let's say a 16-bit Fibonacci LFSR as shown in the corresponding wikipedia article, which generates maximum length sequences, could I use it to create word sequences instead of bit ...
2
votes
1answer
126 views

LFSR get output from characteristic polynomial?

Say you have a characteristic polynomial of an LFSR: $$f(X) = X^4 + X^3 + 1$$ How can I use this function f to get the output of the LFSR, given some initial state? Obviously I can create the LFSR ...
2
votes
1answer
167 views

How to prove this LFSR equation?

I am having difficulty solving part (ii) of Excercise 5.17 from Becker's Cipher Systems. Exercise 5.17 $\quad$If $f(x),g(x)$ are any two polynomials over $GF(2)$ with $f(0)=g(0)=1$ show that ...
2
votes
1answer
47 views

LFSR Output Sampling for Berlekamp-Massey

Looking at the use of Linear Feedback Shift Registers in cryptographic algorithms, I have learned that the Berlekamp-Massey algorithm can be used to find the (shortest) LFSR that generates a given ...
2
votes
1answer
489 views

Linear Feedback Shift Register Taps

Linear feedback shift register tap charts are availale for registers of length 3 to 168. Does anyone have a chart for register lengths from 168 to 256 or beyond? Thank you.
2
votes
1answer
89 views

Berlekamp-Massey to construct minimal LFSR

Given the sequence 0010001111 (or any other, not homework, but exam practice), how do you use the Berlekamp-Massey algorithm to construct a minimal LFSR? I have read several definitions of how ...
2
votes
1answer
103 views

Upper bound Linear Feedback Shift Register

It is clear that when we have any output stream $x_0,x_1,...$ produced by linear feedback shift register than this output has to be periodic. Now I was wondering if we can find an upper bound for ...
2
votes
1answer
130 views

Feasibility of using a base 26 LFSR for cryptography by hand

I have been playing with base 26 LFSRs (i.e. using the alphabet) and noticed that the XOR operation for base 26 is just the tabula recta and so can be done very quickly. This made me wonder whether a ...
1
vote
1answer
68 views

LFSR and Markov chain question

This may seem an elementary question about LFSRs, and their link to Markov chains. LFSRs show Markov chain behaviour in that there can be a transition matrix defined over the LFSR, this follows from ...
1
vote
0answers
45 views

Berlekamp-Massey algorithm, correct stepping

I'm trying to use the Berlekamp-Massey algorithm on the following bit sequence: 0 1 0 0 1 0 0 1 0 1 I have the correct answer and most of the approach to get there, but I'm unable to fill in what I ...
-3
votes
1answer
82 views

What is the best (thoroughly covering) textbook for application of LFSRs in cryptography? [closed]

What is the best (thoroughly covering) textbook for application of LFSRs in cryptography? (Beside Cipher Systems by Beker & Piper)