Fast computation of large distributions and its cryptographic applications
Author
Summary, in English
Let X-1, X-2, ... , X-k be independent n bit random variables. If they have arbitrary distributions, we show how to compute distributions like Pr{X-1 circle plus X-2 circle plus (...) circle plus X-k} and Pr{X-1 boxed plus X-2 boxed plus (...) boxed plus X-k} in complexity O(kn2(n)). Furthermore, if X-1, X-2, ... X-k are uniformly distributed we demonstrate a large class of functions F(X-1, X-2, ... X-k), for which we can compute their distributions efficiently. These results have applications in linear cryptanalysis of stream ciphers as well as block ciphers. A typical example is the approximation obtained when additions modulo 2(n) are replaced by bitwise addition. The efficiency of such an approach is given by the bias of a distribution of the above kind. As an example, we give a new improved distinguishing attack on the stream cipher SNOW 2.0.
Publishing year
2005
Language
English
Pages
313-332
Publication/Series
Lecture Notes in Computer Science
Volume
3788
Document type
Journal article
Publisher
Springer
Topic
- Electrical Engineering, Electronic Engineering, Information Engineering
Keywords
- large distributions
- approximations
- convolution
- algorithms
- cryptanalysis
- complexity
- pseudo-linear functions
Status
Published
ISBN/ISSN/Other
- ISSN: 1611-3349