Algebraic Attacks on Stream Ciphers with Linear Feedback

@inproceedings{Courtois2003AlgebraicAO,
  title={Algebraic Attacks on Stream Ciphers with Linear Feedback},
  author={Nicolas Courtois and Willi Meier},
  booktitle={EUROCRYPT},
  year={2003}
}
A classical construction of stream ciphers is to combine several LFSRs and a highly non-linear Boolean function f . Their security is usually analysed in terms of correlation attacks, that can be seen as solving a system of multivariate linear equations, true with some probability. At ICISC’02 this approach is extended to systems of higher-degree multivariate equations, and gives an attack in 2 for Toyocrypt, a Cryptrec submission. In this attack the key is found by solving an overdefined… Expand
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References

SHOWING 1-10 OF 59 REFERENCES
Fast Algebraic Attacks on Stream Ciphers with Linear Feedback
TLDR
This paper shows how to substantially lower the degree of these equations by multiplying them by well-chosen multivariate polynomials, and is able to break Toyocrypt in 249 CPU clocks, with only 20 Kbytes of keystream, the fastest attack proposed so far. Expand
Higher Order Correlation Attacks, XL Algorithm and Cryptanalysis of Toyocrypt
TLDR
This paper reduces the cryptanalysis of a stream cipher to solving a system of multivariate equations that is overdefined (much more equations than unknowns), and adapts the XL method, introduced at Eurocrypt 2000 for overdefined quadratic systems, to solving equations of higher degree. Expand
Cryptanalysis of Block Ciphers with Overdefined Systems of Equations
TLDR
A new criterion for design of S-boxes in block ciphers should not be describable by a system of polynomial equations that is too small or too overdefined, and this is suggested for both Serpent and Rijndael. Expand
Algebraic Attacks and Decomposition of Boolean Functions
TLDR
Algebraic attacks on LFSR-based stream ciphers recover the secret key by solving an overdefined system of multivariate algebraic equations and become very efficient if such relations of low degrees may be found. Expand
Fast correlation attacks on certain stream ciphers
TLDR
Two new correlation attacks are presented to determine the initial digits of a, provided that the numbert of feedback taps is small, and are demonstrated to be successful against shift registers of considerable lengthk (typically,k=1000). Expand
The Security of Hidden Field Equations (HFE)
We consider the basic version of the asymmetric cryptosystem HFE from Eurocrypt 96.We propose a notion of non-trivial equations as a tentative to account for a large class of attacks on one-wayExpand
Linear Cryptanalysis of Bluetooth Stream Cipher
TLDR
A large class of linear correlations in the Bluetooth combiner, unconditioned or conditioned on the output or on both the output and one input, are found and an attack on the Bluetooth stream cipher that can reconstruct the 128-bit secret key with complexity about 270 from about 45 initializations is proposed. Expand
Attacks based on Conditional Correlations against the Nonlinear Filter Generator
In this paper we extend the conditional correlation attack ([LCPP96]) against the nonlinear filter generator (NLFG) by introducing new conditions and generalisations and present two known-plaintextExpand
Cryptanalytic Time/Memory/Data Tradeoffs for Stream Ciphers
TLDR
This paper shows that a combination of the two approaches has an improved time/memory/data tradeoff for stream ciphers of the form TM2D2 = N2 for any D2 ≤ T ≤ N. Expand
Nonlinearity Criteria for Cryptographic Functions
TLDR
Nonlinearity criteria for Boolean functions are classified in view of their suitability for cryptographic design and two criteria turn out to be of special interest, the distance to linear structures and the Distance to affine functions, which are shown to be invariant under all affine transformations. Expand
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