Berlekamp-Massey algorithm is an algorithm that will find the shortest linear feedback shift register (LFSR) for a given binary output sequence. Here we present. ‘Berlekamp-Massey theorem’ i.e. a recursive construction of the polynomials arising in the Berlekamp-Massey algorithm, relative to any. Often, L is something we want to know in addition to the coefficients. This is where the Berlekamp–Massey algorithm comes in, as it also determines L.

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This the shortest length of an LFSR that reproduces that sequence. We should note here that we totally ignore what it produces after the 8 th symbol — it is not berlekapm — we only care about the first 8 symbols. A very important remark is that our correction cannot cause previous symbols to be incorrect, because then we would have to start all over again.

Practical Cryptography

Let us focus on 1. The false case of the if-statement is pretty obvious — if the LFSR works, do not fix it. First of all, note the following: This linear relation is given by the connection polynomial. Consider the LFSR given byfrom the example above.


Each symbol must fulfill the equationexcept for the symbols that is the starting state of the LFSR. From this, we can define the discrepancy functionwhere for all. Assume that we have a determined the LFSR that produces the correct sequence up to symbol.

Berlekamp-Massey Algorithm Explained

This means we have a series for discrepancies, namely. Clearly, the last one needs to eliminated. How do we do this? How do we construct such a function that also is of lowest possible degree?

Assume that we have made this correction before.

Berlekamp-Massey to construct minimal LFSR – Cryptography Stack Exchange

This means, that at some point, we had an indexwhere the discrepancy function series was. Here, we have found a function that agree with the properties of.

Maasey equation should we use? First note that we need to delay the function steps if we use the discrepancy at index.

Also note that delay is equal to complexity, which we, in turn, want to reduce. Therefore, we want to pick as large as possible, as this, by induction assumption will be minimal. For the BM algorithm to work on arbitrary fieldinstead of adding the previous discrepancy symbolwe have to match it with the current discrepancy. Thus, the correction goes.


See for instance this paper. You are commenting using your WordPress. You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email. Skip to content Menu grocid.

In essence, we can summarize the algorithm into a single for-loop: Note that by changing discrepancy function, we change the connection polynomial.

And this is the correction step of the BM algorithm. For the BM algorithm to work on arbitrary fieldinstead of adding the previous discrepancy symbolwe have to match it with the current discrepancy The following fixes the problem: Leave a Reply Cancel reply Enter your algorithk here Fill in your details below or click an icon to log in: Email required Address never made public.

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