Welcome to the resource topic for 2024/1157
Title:
Shift-invariant functions and almost liftings
Authors: Jan Kristian Haugland, Tron Omland
Abstract:We investigate shift-invariant vectorial Boolean functions on n bits that are lifted from Boolean functions on k bits, for k\leq n. We consider vectorial functions that are not necessarily permutations, but are, in some sense, almost bijective. In this context, we define an almost lifting as a Boolean function for which there is an upper bound on the number of collisions of its lifted functions that does not depend on n. We show that if a Boolean function with diameter k is an almost lifting, then the maximum number of collisions of its lifted functions is 2^{k-1} for any n. Moreover, we search for functions in the class of almost liftings that have good cryptographic properties and for which the non-bijectivity does not cause major security weaknesses. These functions generalize the well-known map \chi used in the Keccak hash function.
ePrint: https://eprint.iacr.org/2024/1157
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