Searching for impossible subspace trails and improved impossible differential characteristics for SIMON-like block ciphers

Xuzi Wang,Dongdai Lin,Baofeng Wu,Lin Hou

doi:10.1186/s42400-021-00081-x

Abstract

In this paper, we greatly increase the number of impossible differentials for SIMON and SIMECK by eliminating the 1-bit constraint in input/output difference, which is the precondition to ameliorate the complexity of attacks. We propose an algorithm which can greatly reduce the searching complexity to find such trails efficiently since the search space exponentially expands to find impossible differentials with multiple active bits. There is another situation leading to the contradiction in impossible differentials except for miss-in-the-middle. We show how the contradiction happens and conclude the precondition of it defined as miss-from-the-middle. It makes our results more comprehensive by applying these two approach simultaneously. This paper gives for the first time impossible differential characteristics with multiple active bits for SIMON and SIMECK, leading to a great increase in the number. The results can be verified not only by covering the state-of-art, but also by the MILP model.

Highlights

Due to the continuously growing impact of RFID tags, smart cards and FPGAs, cryptographic algorithms which are suitable for resource-constrained devices become more and more important
We provide impossible subspace trails for SIMON and SIMECK by searching subspace trails inversely and applying miss-in-the-middle
All existing impossible differential characteristics of SIMON-like block ciphers are obtained with 1-bit constraint either by combining truncated differential and the miss-in-the-middle approach, or by searching automatically using Mixed-integer Linear Programming (MILP)

Summary

Introduction

Due to the continuously growing impact of RFID tags, smart cards and FPGAs, cryptographic algorithms which are suitable for resource-constrained devices become more and more important. We provide impossible subspace trails for SIMON and SIMECK by searching subspace trails inversely and applying miss-in-the-middle. We raise the concept of inverse subspace trail and give its searching algorithms for SIMON-like block ciphers.

Results

Conclusion