On differential properties of pseudo-hadamard transform and related mappings (Extended Abstract)

Abstract

In FSE 2001, Lipmaa and Moriai proposed efficient log-time algorithms for computing some functions that are related to the differential probability of modular addition. They posed it as an open question whether their algorithms can be generalized to more complex functions. In this paper, we will give a fundamentally different proof of their main result by using a more scalable linear-algebraic approach. Our proof technique enables us to easily derive differential probabilities of some other related mappings like the subtraction and the Pseudo-Hadamard Transform. Finally, we show how to apply the derived formulas to analyse partial round mapping of Twofish.