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In LFSR-based stream ciphers, the knowledge of the feedback equation of theLFSR plays a critical role in most attacks. In word-based stream ciphers suchas those in the SNOW series, even if the feedback configuration is hidden,knowing the characteristic polynomial of the state transition matrix of theLFSR enables the attacker to create a feedback equation over $GF(2)$. This, inturn, can be used to launch fast correlation attacks. In this work, we proposea method for hiding both the feedback equation of a word-based LFSR and thecharacteristic polynomial of the state transition matrix. Here, we employ a$z$-primitive $\sigma$-LFSR whose characteristic polynomial is randomly sampledfrom the distribution of primitive polynomials over $GF(2)$ of the appropriatedegree. We propose an algorithm for locating $z$-primitive $\sigma$-LFSRconfigurations of a given degree. Further, an invertible matrix is generatedfrom the key. This is then employed to generate a public parameter which isused to retrieve the feedback configuration using the key. If the key size is$n$- bits, the process of retrieving the feedback equation from the publicparameter has a average time complexity $\mathbb{O}(2^{n-1})$. The proposedmethod has been tested on SNOW 2.0 and SNOW 3G for resistance to fastcorrelation attacks. We have demonstrated that the security of SNOW 2.0 andSNOW 3G increases from 128 bits to 256 bits.

A Scheme to resist Fast Correlation Attack for Word Oriented LFSR based Stream Cipher