An algebraic attack on the improved summation generator with 2-bit memory

Recently algebraic attacks on stream ciphers have received much attention. In this paper we apply an algebraic attack to the improved summation generator with 2-bit memory, which was presented by Lee and Moon in order to give the original summation generator correlation immunity. We show that the initial state of the generator can be recovered within O(n5.6) bit operations from O(n2) regular output bits, where n is the total length of LFSRs. We could recover the initial key bits in practice within 3 minutes on a PC even for the case n=256. Our result is a good example that shows how powerful algebraic attacks are in the analysis of stream ciphers.