Generalizing and characterizing shift-invariant maps for lightweight cryptography
A generalization of the map $χ$
Information Theory
Summary
The authors study a special type of function used in lightweight cryptography, which helps secure data on small devices. They look at a known function that mixes bits in a specific way and then find all the possible similar functions doing the same kind of mixing. Their work helps understand the full range of such functions that keep things balanced and stable over shifts and have a certain mathematical complexity.
What this means in practice
- •For cryptography engineers: Design more secure or efficient lightweight cryptographic components by knowing all possible shift-invariant degree-2 mappings.
- •For hardware security teams: Evaluate and implement novel bit-mixing functions that maintain security properties across shifts in hardware design.
A theory result. No direct application yet.
Authors
Xiutao Feng, Qiang Wang, Jingyi Yu, Anpeng Zhang
Abstract
The mapping $ χ_n:\mathbb{F}_2^n \to \mathbb{F}_2^n$ defined by $y=χ_n(x)$ with $y_i = x_i + x_{i+1}x_{i+2} + x_{i+2}$, where the indices are computed modulo $n$, has been widely studied for its application in lightweight cryptography. In this paper, we generalize this mapping and completely characterize all these shift-invariant permutations of algebraic degree $2$.