Abstract
Designers of stream ciphers have generally used ad hoc meth- ods to build systems that are secure against known attacks. There is often a sense that this is the best that can be done, that any system will even- tually fall to a practical attack. In this paper we show that there are families of keystream generators that resist all possible attacks of a very general type in which a small number of known bits of a keystream are used to synthesize a generator of the keystream (called a synthesizing algorithm). Such attacks are exemplified by the Berlekamp-Massey at- tack. We first formalize the notions of a family of feedback registers and of a synthesizing algorithm. We then show that for any function h(n) that is in O(2n/d) for every d > 0, there is a secure family B of periodic sequences in the sense that any efficient synthesizing algorithm outputs a register of size h(log(period(B))) given the required number of bits of a sequence B ∈ B of large enough period. This result is tight in the sense it fails for any faster growing function h(n). We also consider several variations on this scenario.
This research funded in part by NSF grant #NCR-9400762.
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Klapper, A. (1996). On the Existence of Secure Feedback Registers. In: Maurer, U. (eds) Advances in Cryptology — EUROCRYPT ’96. EUROCRYPT 1996. Lecture Notes in Computer Science, vol 1070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68339-9_23
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DOI: https://doi.org/10.1007/3-540-68339-9_23
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