shrinking generator is proposed. Key words: Stream cipher, pseudorandom sequence, linear complexity,. Geffe’s generator, Geffe’s shrinking. Geffe generator [5] is a non-linear random binary key sequence generator which consists of three (LFSRs) and a nonlinear combiner. Here, we. Request PDF on ResearchGate | Cryptanalysis of Geffe Generator Using Genetic Algorithm | The use of basic crypto-primitives or building blocks has a vital role.

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For example, a Boolean function which has no first order or second order correlations but which does have a third order correlation exhibits 2nd order correlation immunity. Correlation attacks exploit a statistical weakness that arises from a poor choice of the Boolean function — it is possible to select a function which avoids correlation attacks, so this type of cipher henerator not inherently insecure.

Obviously, higher correlation immunity makes a function more suitable for use in a keystream generator although this is not the only thing which needs to be considered.

If we had, say, a megabyte of known plaintext, the situation would be substantially different. Views Read Edit View history.

Compared to the cost of launching a brute force attack on the entire system, with complexity 2 32this represents an attack effort saving factor of just underwhich is substantial. The following steps are repeated until a keystream of desired length is produced.

If you want the generator to have gfnerator statistical properties and be quite secured, the length of the three primitive polynomial must be relatively prime pairwise and also the length of all LFSRs should be at least bits. This is not as improbable as it may seem: Thus we say that LFSR-3 is correlated with the generator.

Correlation attack

Readers with a background in probability theory should be able to see easily how to formalise this argument and obtain estimates of the length of known plaintext required for a given correlation using the binomial distribution. Research has been conducted into methods for easily generating Boolean functions of genertor given size which are guaranteed to have at least some particular order of correlation immunity.

It is possible to define higher order correlations in addition to these. This also follows from the fact that any such function can be written using a Reed-Muller basis as a combination of XORs of the input functions.


The Geffe generator Modern stream ciphers are inspired from one-time pad. To create a maximal length sequence, the lengths of the three primitive polynomial must be relatively prime pairwise. As a rule, the weaker the correlation between an individual register and the generator output, the more known plaintext is required to find that register’s key with a high degree of confidence. Wikipedia articles with style issues from October All articles with style issues All articles with unsourced statements Articles with unsourced statements from July Articles to be expanded from October All articles to be expanded Articles using small message boxes.

Let’s check this quickly: There are other issues to consider, e. The table below shows a measure of the computational cost for various attacks on a keystream generator consisting of eight 8-bit LFSRs combined by a single Boolean function.

While higher order correlations lead to more powerful attacks, they are also more difficult to find, as the space of available Boolean functions to correlate against the generator output increases as the number of arguments to the function does.

In practice it may be difficult to find a function which achieves this without sacrificing other design criteria, e. The clock-controlled generator In nonlinear combination keystream generators Geffe generatorthe linear feedback shift registers are clocked regularly and so all the LFSRs are controlled by the same clock.

Click the image to getfe it larger in a new window You should copy, paste each VHDL code in your editor and then name each file exactly as shown below: Click each image to view it larger in a new window. Stream ciphers convert plaintext to ciphertext one gensrator at a time and are often constructed using two or more LFSRs.

History of cryptography Cryptanalysis Outline of cryptography. An incorrect key may generate LFSR output that agrees with more than kilobytes of the generator output, but not likely to generate output that agrees with as much as kilobytes of the generator output like a correctly guessed key would.

Click each image to view it larger in a new window 2- A more advanced stream cipher: Because the use of LFSR alone is insufficient to provide good security, keystream generator combines outputs of linear feedback shift registers in parallel using mainly three different methods: Thus, we are able to break the Geffe generator with as much effort as required to brute force 3 entirely independent LFSRs, meaning that the Geffe generator is a very weak generator and should never be used to generate stream cipher keystreams.


The correlations which were exploited in the example attack on the Geffe generator are examples of what are called first order correlations: When R1 is clocked, if its output is 0 then R3 is clocked and its output is XORed with the previous state of R2 which has not been clocked.

This is a weakness we may exploit as follows:. This section needs expansion. RC4 block ciphers in stream mode ChaCha. Combined with partial knowledge of the keystream which is easily derived from partial knowledge of the plaintext, as the two are simply XORed togetherthis allows an attacker to brute-force the key for that individual LFSR and the rest of the system separately.

This would be an example of a second order correlation. This article’s tone or style may not reflect the encyclopedic tone used on Wikipedia.

Correlation attack – Wikipedia

Symmetric-key algorithm Block cipher Stream cipher Public-key cryptography Cryptographic hash function Message authentication code Random numbers Steganography. This research has uncovered links between correlation immune Boolean functions and error correcting codes. October Learn how and when to remove this template message. We will consider the case of the Generstor keystream generator.

Block ciphers security summary. Let’s have a close look at this Geffe generator: Suppose further that we know some part of the plaintext, e. Similar to this, many file formats or network protocols have standard headers or footers which can be guessed easily.

Retrieved from ” https: Then these LFSRs become irregularly clocked.

Beaglebone and more

We can define third order correlations and so on in the obvious way. Correlation attacks are perhaps best explained via example. In this sense, correlation attacks can be considered divide and conquer algorithms. We now know 32 consecutive bits of the generator output.

Collision attack Preimage attack Birthday attack Brute-force attack Rainbow table Side-channel attack Length extension attack. Thus we may not be able to find the key for that LFSR uniquely and with certainty.