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.
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.