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Implementation of Berlekamp-Massey Algorithm

, 15 Sep 2005 CPOL
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Implementation of Berlekamp-Massey algorithm


The Berlekamp-Massey algorithm is an efficient algorithm for determining the linear complexity of a finite binary sequence sn of length n. The algorithm takes n iterations, with the Nth iteration computing the linear complexity of the subsequence sN consisting of the first N terms of sn. Returned value (L) is the length of the shortest linear feedback shift register sequence that generates all bits in sequence sn.
(Used in NIST statistical test suite - "Linear Complexity Test".)

The Code

    // Implementation of Berlekamp-Massey algorithm for calculating linear 
    // complexity of binary sequence
    // s = byte array with binary sequence
    // returns Length of LFSR with smallest length which generates s
    // for an example: int L=BerlekampMassey(new byte[] {1,0,1,0,1,1,1,0,1,0})
    //        reference: "Handbook of Applied Cryptography", p201

    public static int BerlekampMassey(byte[] s)                
        int L, N, m, d;
        int n=s.Length;
        byte[] c=new byte[n];
        byte[] b=new byte[n];
        byte[] t=new byte[n];

        //Algorithm core
        while (N<n)
            for (int i=1; i<=L; i++)
            d^=c[i]&s[N-i];            //(d+=c[i]*s[N-i] mod 2)
            if (d==1)
                Array.Copy(c, t, n);    //T(D)<-C(D)
                for (int i=0; (i+N-m)<n; i++)
                if (L<=(N>>1))
                    Array.Copy(t, b, n);    //B(D)<-T(D)
        return L;


Sorry, but this might only be useful to those freaks (like meSmile | :) that work on statistical tests and/or cryptanalysis. I just needed to put this on the Web because I couldn't find some useful implementation out there.


This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)


About the Author

Miroslav Stampar
Software Developer (Senior)
Croatia Croatia
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Comments and Discussions

Generalberelekamp massey Pinmemberraza817-May-09 12:37 
GeneralJust Curious PinmemberJohnDeHope315-Sep-05 5:18 
GeneralRe: Just Curious Pinmembervadivhere15-Sep-05 8:10 
GeneralRe: Just Curious PinmemberMiroslav Stampar15-Sep-05 23:47 

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