Summarising recent results on finding multiples of primitive polynomials over GF(2)

Summarising recent results, we emphasise the importance of studying the. properties of multiples of primitive polynomials and their products in connection with fast correlation attacks on LFSR-based stream cipher systems. These results may serve as an important tool for future design of stream cipher systems with LFSR as a main design block. Also the security of such existing systems needs to be reviewed in light of these results. Finding an efficient polynomial time algorithm to get the least degree t-nomial multiple of the primitive polynomials and their products is still an open problem.