Paper 2001/092
BDD-based Cryptanalysis of Keystream Generators
Matthias Krause
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.
Metadata
- Available format(s)
-
PDF PS
- Category
- Secret-key cryptography
- Publication info
- Published elsewhere. still not published but submitted
- Keywords
- stream ciphers
- Contact author(s)
- krause @ th informatik uni-mannheim de
- History
- 2001-11-06: received
- Short URL
- https://ia.cr/2001/092
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2001/092,
author = {Matthias Krause},
title = {{BDD}-based Cryptanalysis of Keystream Generators},
howpublished = {Cryptology {ePrint} Archive, Paper 2001/092},
year = {2001},
url = {https://eprint.iacr.org/2001/092}
}