Higher-Order Differential Properties of Keccak and Luffa
- Cite this paper as:
- Boura C., Canteaut A., De Cannière C. (2011) Higher-Order Differential Properties of Keccak and Luffa. In: Joux A. (eds) Fast Software Encryption. FSE 2011. Lecture Notes in Computer Science, vol 6733. Springer, Berlin, Heidelberg
In this paper, we identify higher-order differential and zero-sum properties in the full Keccak-f permutation, in the Luffa v1 hash function and in components of the Luffa v2 algorithm. These structural properties rely on a new bound on the degree of iterated permutations with a nonlinear layer composed of parallel applications of a number of balanced Sboxes. These techniques yield zero-sum partitions of size 21575 for the full Keccak-f permutation and several observations on the Luffa hash family. We first show that Luffa v1 applied to one-block messages is a function of 255 variables with degree at most 251. This observation leads to the construction of a higher-order differential distinguisher for the full Luffa v1 hash function, similar to the one presented by Watanabe et al. on a reduced version. We show that similar techniques can be used to find all-zero higher-order differentials in the Luffa v2 compression function, but the additional blank round destroys this property in the hash function.