Metadata-Version: 2.1
Name: pylfsr
Version: 1.0.6
Summary: Linear Feedback Shift Register
Home-page: https://github.com/Nikeshbajaj/Linear_Feedback_Shift_Register
Author: Nikesh Bajaj
Author-email: nikkeshbajaj@gmail.com
License: MIT
Download-URL: https://github.com/Nikeshbajaj/Linear_Feedback_Shift_Register/tarball/1.0.6
Description: # LFSR -Linear Feedback Shift Register
        
        
        ## Links: **[Github Page](http://nikeshbajaj.github.io/Linear_Feedback_Shift_Register/)** | **[Documentation](https://lfsr.readthedocs.io/)** | **[Github](https://github.com/Nikeshbajaj/Linear_Feedback_Shift_Register)**  |  **[PyPi - project](https://pypi.org/project/pylfsr/)** |     _ **Installation:** [pip install pylfsr](https://pypi.org/project/pylfsr/)
        -----
        
        
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        <p align="center">
          <img src="https://raw.githubusercontent.com/nikeshbajaj/Linear_Feedback_Shift_Register/master/images/LFSR.jpg" width="400"/>
          <img src="https://raw.githubusercontent.com/nikeshbajaj/Linear_Feedback_Shift_Register/master/images/5bit_8.gif" width="500"/>
        </p>
        
        -----
        ## Table of contents
        - [**New Updates**](#new-updates)
        - [**Installation**](#installation)
        - [**Examples**](#examples)
            - [**5-bit LFSR**](#example-1-5-bit-lfsr-with-feedback-polynomial-x5--x2--1)
            - [**Vizualize each state**](#example-3--to-visualize-the-process-with-3-bit-lfsr-with-default-counter_start_zero--true)
            - [**Plot your LFSR**](#visulizeplot-your-lfsr)
            - [**Test properties of LFSR**](#example-6--testing-the-properties)
        - [**A5/1 GSM Stream Cipher**](#a51-gsm-stream-cipher-generator)
        - [**Geffe Genegerator**](#geffe-generator)
        - [**Matlab Implementation**](#matlab)
        -----
        
        ## New Updates
        ## Plot Your LFSR with pylfsr
        <p align="center">
          <img src="https://raw.githubusercontent.com/nikeshbajaj/Linear_Feedback_Shift_Register/master/images/5bit_6.gif" width="800"/>
        </p>
        
        ## Updates:
          - Fixed the bugs (1) missing initial bit (2) exception
          - **Added test properties of LFSR**
        	  -   **(1) Balance Property**
        	  -   **(2) Runlength Property**
        	  -   **(3) Autocorrelation Property**
          -  **Ploting function to display LFSR**
          -  **A5/1 GSM Stream Ciper Generator**
          -  **Geffe Generator**
        
        
        # Installation
        
        ## Requirement : *numpy*, *matplotlib*
        
        ### with pip
        
        ```
        pip install pylfsr
        ```
        
        
        ### Build from the source
        Download the repository or clone it with git, after cd in directory build it from source with
        
        ```
        python setup.py install
        ```
        
        ## Examples
        ### **Example 1**: 5-bit LFSR with feedback polynomial *x^5 + x^2 + 1*
        
        ```
        # import LFSR
        import numpy as np
        from pylfsr import LFSR
        
        L = LFSR()
        
        # print the info
        L.info()
        
        5 bit LFSR with feedback polynomial  x^5 + x^2 + 1
        Expected Period (if polynomial is primitive) =  31
        Current :
        State        :  [1 1 1 1 1]
        Count        :  0
        Output bit   : -1
        feedback bit : -1
        ```
        
        
        ```
        L.next()
        L.runKCycle(10)
        L.runFullCycle()
        L.info()
        ```
        
        ### Example 2**: 5-bit LFSR with custum state and feedback polynomial
        
        ```
        state = [0,0,0,1,0]
        fpoly = [5,4,3,2]
        L = LFSR(fpoly=fpoly,initstate =state, verbose=True)
        L.info()
        tempseq = L.runKCycle(10)
        L.set(fpoly=[5,3])
        ```
        
        ### Example 3 ## To visualize the process with 3-bit LFSR, with default counter_start_zero = True
        ```
        state = [1,1,1]
        fpoly = [3,2]
        L = LFSR(initstate=state,fpoly=fpoly)
        print('count \t state \t\toutbit \t seq')
        print('-'*50)
        for _ in range(15):
            print(L.count,L.state,'',L.outbit,L.seq,sep='\t')
            L.next()
        print('-'*50)
        print('Output: ',L.seq)
        ```
        Output :
        
        ```
        count 	        state 		outbit 	 seq
        --------------------------------------------------
        0		[1 1 1]		-1	[-1]
        1		[0 1 1]		1	[1]
        2		[0 0 1]		1	[1 1]
        3		[1 0 0]		1	[1 1 1]
        4		[0 1 0]		0	[1 1 1 0]
        5		[1 0 1]		0	[1 1 1 0 0]
        6		[1 1 0]		1	[1 1 1 0 0 1]
        7		[1 1 1]		0	[1 1 1 0 0 1 0]
        8		[0 1 1]		1	[1 1 1 0 0 1 0 1]
        9		[0 0 1]		1	[1 1 1 0 0 1 0 1 1]
        10		[1 0 0]		1	[1 1 1 0 0 1 0 1 1 1]
        11		[0 1 0]		0	[1 1 1 0 0 1 0 1 1 1 0]
        12		[1 0 1]		0	[1 1 1 0 0 1 0 1 1 1 0 0]
        13		[1 1 0]		1	[1 1 1 0 0 1 0 1 1 1 0 0 1]
        14		[1 1 1]		0	[1 1 1 0 0 1 0 1 1 1 0 0 1 0]
        --------------------------------------------------
        Output:  [1 1 1 0 0 1 0 1 1 1 0 0 1 0 1]
        ```
        
        ### Example 4 ## To visualize the process with 3-bit LFSR, with default counter_start_zero = False
        ```
        state = [1,1,1]
        fpoly = [3,2]
        L = LFSR(initstate=state,fpoly=fpoly,counter_start_zero=False)
        print('count \t state \t\toutbit \t seq')
        print('-'*50)
        for _ in range(15):
            print(L.count,L.state,'',L.outbit,L.seq,sep='\t')
            L.next()
        print('-'*50)
        print('Output: ',L.seq)
        ```
        
        Output
        ```
        count 	 state 		outbit 	 seq
        --------------------------------------------------
        1	[1 1 1]		1	[1]
        2	[0 1 1]		1	[1 1]
        3	[0 0 1]		1	[1 1 1]
        4	[1 0 0]		0	[1 1 1 0]
        5	[0 1 0]		0	[1 1 1 0 0]
        6	[1 0 1]		1	[1 1 1 0 0 1]
        7	[1 1 0]		0	[1 1 1 0 0 1 0]
        8	[1 1 1]		1	[1 1 1 0 0 1 0 1]
        9	[0 1 1]		1	[1 1 1 0 0 1 0 1 1]
        10	[0 0 1]		1	[1 1 1 0 0 1 0 1 1 1]
        11	[1 0 0]		0	[1 1 1 0 0 1 0 1 1 1 0]
        12	[0 1 0]		0	[1 1 1 0 0 1 0 1 1 1 0 0]
        13	[1 0 1]		1	[1 1 1 0 0 1 0 1 1 1 0 0 1]
        14	[1 1 0]		0	[1 1 1 0 0 1 0 1 1 1 0 0 1 0]
        --------------------------------------------------
        Output:  [1 1 1 0 0 1 0 1 1 1 0 0 1 0 1]
        ```
        
        ## Visulize/Plot your LFSR
        ```
        L.Viz(show=False, show_labels=False,title='R1')
        
        ```
        
        <p align="center">
          <img src="https://raw.githubusercontent.com/nikeshbajaj/Linear_Feedback_Shift_Register/master/images/5bit_0.jpg" width="500"/>
        </p>
        
        
        
        ## Example 5  ## 23 bit LFSR with custum state and feedback polynomial
        ```
        fpoly = [23,19]
        L1 = LFSR(fpoly=fpoly,initstate ='ones', verbose=False)
        L1.info()
        ```
        Output
        ```
        23 bit LFSR with feedback polynomial  x^23 + x^19 + 1
        Expected Period (if polynomial is primitive) =  8388607
        Current :
         State        :  [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
         Count        :  0
         Output bit   :  -1
         feedback bit :  -1
        ```
        ```
        seq = L1.runKCycle(100)
        ```
        
        ```seq
        array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
        1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
        1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1,
        1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
        1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1])
        ```
        ##  Example 6 ## testing the properties
        ```
        state = [1,1,1,1,0]
        fpoly = [5,3]
        L = LFSR(initstate=state,fpoly=fpoly)
        result  = L.test_properties(verbose=2)
        ```
        Output
        ```
        1. Periodicity
        ------------------
         - Expected period = 2^M-1 = 31
         - Pass?:  True
        
        2. Balance Property
        -------------------
         - Number of 1s = Number of 0s+1 (in a period): (N1s,N0s) =  (16, 15)
         - Pass?:  True
        
        3. Runlength Property
        -------------------
         - Number of Runs in a period should be of specific order, e.g. [4,2,1,1]
         - Runs:  [8 4 2 1 1]
         - Pass?:  True
        
        4. Autocorrelation Property
        -------------------
         - Autocorrelation of a period should be noise-like, specifically, 1 at k=0, -1/m everywhere else
         - Pass?:  True
        
        ==================
        Passed all the tests
        ==================
        ```
        <p align="center">
          <img src="https://raw.githubusercontent.com/nikeshbajaj/Linear_Feedback_Shift_Register/master/images/acorr_test.jpg" width="500"/>
        </p>
        
        Testing individual property
        ```
        # get a full period sequence
        p = L.getFullPeriod()
        p
        array([0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0,
               0, 1, 0, 0, 1, 0, 1, 1, 0])
        ```
        
        ```
        L.balance_property(p.copy())
        # (True, (16, 15))
        
        L.runlength_property(p.copy())
        # (True, array([8, 4, 2, 1, 1]))
        
        L.autocorr_property(p.copy())[0]
        #True
        ```
        
        ##  Example 7 ## testing the properties for non-primitive polynomial
        ```
        state = [1,1,1,1,0]
        fpoly = [5,1]
        L = LFSR(initstate=state,fpoly=fpoly)
        result = L.test_properties(verbose=1)
        ```
        Output
        ```
        1. Periodicity
        ------------------
         - Expected period = 2^M-1 = 31
         - Pass?:  False
        
        2. Balance Property
        -------------------
         - Number of 1s = Number of 0s+1 (in a period): (N1s,N0s) =  (17, 14)
         - Pass?:  False
        
        3. Runlength Property
        -------------------
         - Number of Runs in a period should be of specific order, e.g. [4,2,1,1]
         - Runs:  [10  2  1  1  2]
         - Pass?:  False
        
        4. Autocorrelation Property
        -------------------
         - Autocorrelation of a period should be noise-like, specifically, 1 at k=0, -1/m everywhere else
         - Pass?:  False
        
        ==================
        Failed one or more tests, check if feedback polynomial is primitive polynomial
        ==================
        ```
        <p align="center">
          <img src="https://raw.githubusercontent.com/nikeshbajaj/Linear_Feedback_Shift_Register/master/images/acorr_test_npf.jpg" width="500"/>
        </p>
        
        
        ### Example 8**: Get the feedback polynomial or list
        Reference : http://www.partow.net/programming/polynomials/index.html
        
        ```
        L = LFSR()
        # list of 5-bit feedback polynomials
        fpoly = L.get_fpolyList(m=5)
        
        # list of all feedback polynomials as a dictionary
        fpolyDict = L.get_fpolyList()
        ```
        
        
        ### Changing feedback polynomial in between
        ```
        L.changeFpoly(newfpoly =[23,14],reset=False)
        seq1 = L.runKCycle(20)
        
        # Change after 20 clocks
        L.changeFpoly(newfpoly =[23,9],reset=False)
        seq2 = L.runKCycle(20)
        ```
        
        # A5/1 GSM Stream cipher generator
        <p align="center">
          <img src="https://upload.wikimedia.org/wikipedia/commons/5/5e/A5-1_GSM_cipher.svg" width="500"/>
        </p>
        
        Ref: https://en.wikipedia.org/wiki/A5/1
        
        ```
        import numpy as np
        import matplotlib.pyplot as plt
        from pylfsr import A5_1
        
        A5 = A5_1(key='random')
        print('key: ',A5.key)
        A5.R1.Viz(title='R1')
        A5.R2.Viz(title='R2')
        A5.R3.Viz(title='R3')
        
        print('key: ',A5.key)
        print()
        print('count \t cbit\t\tclk\t R1_R2_R3\toutbit \t seq')
        print('-'*80)
        for _ in range(15):
            print(A5.count,A5.getCbits(),A5.clock_bit,A5.getLastbits(),A5.outbit,A5.getSeq(),sep='\t')
            A5.next()
        print('-'*80)
        print('Output: ',A5.seq)
        
        A5.runKCycle(1000)
        A5.getSeq()
        
        ```
        
        
        ## Enhanced A5/1
        
        Reference Article: **Enhancement of A5/1**: https://doi.org/10.1109/ETNCC.2011.5958486
        
        ```
        # Three LFSRs initialzed with 'ones' though they are intialized with encription key
        R1 = LFSR(fpoly = [19,18,17,14])
        R2 = LFSR(fpoly = [23,22,21,8])
        R3 = LFSR(fpoly = [22,21])
        
        # clocking bits
        b1 = R1.state[8]
        b2 = R3.state[10]
        b3 = R3.state[10]
        
        ```
        
        
        
        # Geffe Generator
        <p align="center">
          <img src="https://raw.githubusercontent.com/nikeshbajaj/Linear_Feedback_Shift_Register/master/images/Geffe_0.jpg" width="500"/>
        </p>
        
        Ref: Schneier, Bruce. Applied cryptography: protocols, algorithms, and source code in C. john wiley & sons, 2007.
        	Chaper 16
        
        ```
        import numpy as np
        import matplotlib.pyplot as plt
        from pylfsr import Geffe, LFSR
        
        kLFSR = [LFSR(initstate='random') for _ in range(8)]
        cLFSR = LFSR(initstate='random')
        
        GG = Geffe(kLFSR_list=kLFSR, cLFSR=cLFSR)
        
        print('key: ',GG.getState())
        print()
        for _ in range(50):
            print(GG.count,GG.m_count,GG.outbit_k,GG.sel_k,GG.outbit,GG.getSeq(),sep='\t')
            GG.next()
        
        GG.runKCycle(1000)
        GG.getSeq()
        ```
        
        
        
        
        _______________________________________________________________________________________________
        
        # MATLAB
        ## For matlab files download it from here
        Folder : https://github.com/Nikeshbajaj/Linear_Feedback_Shift_Register/tree/master/matlabfiles
        
        **Description**
        Genrate randon binary sequence using LFSR for any given feedback taps (polynomial),
        This will also check Three fundamental Property of LFSR
        1. Balance Property
        2. Runlength Property
        3. Autocorrelation Property
        
        **This MATLAB Code work for any length of LFSR with given taps (feedback polynomial) -Universal, There are three files LFSRv1.m an LFSRv2.m, LFSRv3.m**
        
        ### LFSRv1
        This function will return all the states of LFSR and will check Three fundamental Property of LFSR
        (1) Balance Property (2) Runlength Property (3) Autocorrelation Property
        
        #### EXAMPLE
        ```
        s=[1 1 0 0 1]
        t=[5 2]
        [seq c] =LFSRv1(s,t)
        ```
        
        ### LFSRv2
        This function will return only generated sequence will all the states of LFSR, no verification of properties are done
        here. Use this function to avoid verification each time you execute the program.
        #### EXAMPLE
        ```
        s=[1 1 0 0 1]
        t=[5 2]
        [seq c] =LFSRv2(s,t)
        ```
        
        ### LFSRv3 (faster)
        *seq = LFSRv3(s,t,N)*
        this function generates N bit sequence only. This is faster then other two functions, as this does not gives each state of LFSR
        
        #### EXAMPLE
        ```
        s=[1 1 0 0 1]  
        t=[5 2]
        seq =LFSRv3(s,t,50)
        ```
        
        
        
        ## Tips
        * If you want to use this function in middle of any program, use LFSRv2 or LFSRv1 with verification =0.
        * If you want to make it fast for long length of LFSR,use LFSRv3.m
        
        ______________________________________
        
        # Contacts:
        
        If any doubt, confusion or feedback please contact me
        * **Nikesh Bajaj**
        * http://nikeshbajaj.in
        * n.bajaj@qmul.ac.uk
        * bajaj[dot]nikkey [AT]gmail[dot]com
        ### PhD Student: Queen Mary University of London & University of Genoa
        ______________________________________
        
Keywords: lfsr linear-feedback-shift-register random generator gf(2) A5/1 GSM-stream-cipher stream-cipher Geffe-Generator
Platform: UNKNOWN
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.5
Classifier: Programming Language :: Python :: 3.6
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