Dear all,
Next week, we have the pleasure of having Prof. Orr Dunkelman give a talk
in the colloquium.
The seminar will be held on Monday, June 3rd at 14:00.
Location: C221.
The title, abstract and bio appear below.
Looking forward to seeing you,
Sagie and Liat
*Title:*
The Hunt for High Probability Statistical Impurities in Cryptographic
Primitives
*Abstract:*
Computer security relies on cryptographic primitives such as block ciphers
and hash functions. The security of these primitives is usually not proved
in a reduction-style proof, but rather argued based on claims of the form -
this block cipher has no statistical property of some type (e.g.,
differential) with high enough probability. However, how do we know that
there are no such statistical properties in a given n-bit cryptographic
primitive?
When *n* is small (e.g., an 8-bit S-box), this is easy to do. However, for
large values of *n*, the only practical way to find such statistical
properties was to exploit the internal structure of the primitive and to
speed up the search with a variety of heuristic rules of thumb. However,
such bottom-up techniques can miss many properties, especially in
cryptosystems which are designed to have hidden trapdoors.
In this work we consider the top-down version of the problem in which the
cryptographic primitive is given as a structureless black box, and reduce
the complexity of the best known techniques for finding all its significant
differential and linear properties by a large factor of 2^{n/2}. Our main
new tool is the idea of using *surrogate differentiation*. In the context
of finding differential properties, it enables us to simultaneously find
information about all the differentials of the form f(x) \oplus f(x \oplus
\alpha) in all possible directions by differentiating *f* in a single
randomly chosen direction \gamma (which is unrelated to the \alpha’s). In
the context of finding linear properties, surrogate differentiation can be
combined in a highly effective way with the Fast Fourier Transform. For
64-bit cryptographic primitives, this technique makes it possible to
automatically find in about 2^64 time all their differentials with
probability larger than 2^{-32} and all their linear approximations with
bias larger than 2^{-16}; previous algorithms for these problems required
at least 2^{96} time.
This is a joint work with Itai Dinur, Nathan Keller, Eyal Ronen, and Adi
Shamir.
*Bio*:
Orr Dunkelman is a full professor in the Computer Science Department at the
University of Haifa. He has held post-doctoral research positions at the
Weizmann Institute of Science, Ecole Normale Superieure, and Katholieke
Universiteit Leuven. He earned his Ph.D. from the Technion under the
supervision of Prof. Eli Biham.