Large-scale S-box design and analysis of SPS structure - Lan ZHANG; Liangsheng HE; Bin YU (Tongxin xuebao)
A class of optimal linear transformation P over a finite field ( <msubsup> F 2 m </msubsup> ) 4 was constructed based on cyclic shift and XOR operation.Using the idea of inverse proof of input-output relation of linear transformation for reference, a proof method was put forward that transformed the objective problem of optimal linear transformation into several theorems of progressive relation, which not only solved the proof of that kind of optimal linear transformation, but also was suitable for the proof of any linear transformation.By means of small-scale S-box and optimal cyclic shift-XOR linear transformation P, a large-scale S-box model with 2-round SPS structure was established, and a series of lightweight large-scale S-boxes with good cryptographic properties were designed.Only three kind of basic operations such as look-up table, cyclic shift and XOR were used in the proposed design scheme, which improved the linearity and difference uniformity of large-scale S-boxes.Theoretical proof and case analysis show that, compared with the existing large-scale S-box construction methods, the proposed large-scale S-box design scheme has lower computational cost and better cryptographic properties such as difference and linearity, which is suitable for the design of nonlinear permutation coding of lightweight cryptographic algorithms.