Correlation properties of combiners with memory in stream ciphers
Journal of Cryptology - Eurocrypt '90
On an improved summation generator with 2-bit memory
Signal Processing
Cryptanalysis of Summation Generator
ASIACRYPT '92 Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Higher order correlation attacks, XL algorithm and cryptanalysis of Toyocrypt
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Algebraic attacks on stream ciphers with linear feedback
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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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(n^5^.^6) bit operations from O(n^2) 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.