CryptoDB
BDD-based Cryptanalysis of Keystream Generators
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| Abstract: | Many of the keystream generators which are used in practice are LFSR-based in the sense that they produce the keystream according to a rule $y=C(L(x))$, where $L(x)$ denotes an internal linear bitstream, produced by a small number of parallel linear feedback shift registers (LFSRs), and $C$ denotes some nonlinear compression function. We present an $n^{O(1)} 2^{(1-\alpha)/(1+\alpha)n}$ time bounded attack, the FBDD-attack, against LFSR-based generators, which computes the secret initial state $x\in\booln$ from $cn$ consecutive keystream bits, where $\alpha$ denotes the rate of information, which $C$ reveals about the internal bitstream, and $c$ denotes some small constant. The algorithm uses Free Binary Decision Diagrams (FBDDs), a data structure for minimizing and manipulating Boolean functions. The FBDD-attack yields better bounds on the effective key length for several keystream generators of practical use, so a $0.656n$ bound for the self-shrinking generator, a $0.6403 n$ bound for the A5/1 generator, used in the GSM standard, a $0.6n$ bound for the $E_0$ encryption standard in the one level mode, and a $0.8823n$ bound for the two-level $E_0$ generator used in the Bluetooth wireless LAN system. |
BibTeX
@misc{eprint-2001-11504,
title={BDD-based Cryptanalysis of Keystream Generators},
booktitle={IACR Eprint archive},
keywords={secret-key cryptography / stream ciphers},
url={http://eprint.iacr.org/2001/092},
note={still not published but submitted krause@th.informatik.uni-mannheim.de 11632 received 6 Nov 2001},
author={Matthias Krause},
year=2001
}