Further Observations on SIMON and SPECK Block Cipher Families

Seyed Dehnavi

doi:10.3390/cryptography3010001

Abstract

SIMON and SPECK families of block ciphers are well-known lightweight ciphers designed by the NSA. In this note, based on the previous investigations on SIMON, a closed formula for the squared correlations and differential probabilities of the mapping ϕ ( x ) = x ⊙ S 1 ( x ) on F 2 n is given. From the aspects of linear and differential cryptanalysis, this mapping is equivalent to the core quadratic mapping of SIMON via rearrangement of coordinates and EA -equivalence. Based on the proposed explicit formula, a full description of DDT and LAT of ϕ is provided. In the case of SPECK, as the only nonlinear operation in this family of ciphers is addition mod 2 n , after reformulating the formula for linear and differential probabilities of addition mod 2 n , straightforward algorithms for finding the output masks with maximum squared correlation, given the input masks, as well as the output differences with maximum differential probability, given the input differences, are presented. By the aid of the tools given in this paper, the process of the search for linear and differential characteristics of SIMON and SPECK families of block ciphers could be sped up, and the complexity of linear and differential attacks against these ciphers could be reduced.

Highlights

SIMON and SPECK are two families of block ciphers that were designed by the NSA [1].These lightweight ciphers have widely attracted the attention of researchers [2,3,4,5,6,7,8,9,10,11,12,13,14]
The method of the research of this paper is somewhat similar to [15,16,17,18,19,20,21,22,23,24]: we study the linear and differential properties of the components of SIMON and SPECK families of block ciphers, from the mathematical viewpoint
Of φ, which in turn leads to the full determination of Difference Distribution Table (DDT) and Linear Approximation Table (LAT) of the core quadratic mapping of SIMON, as well as the straightforward algorithms for finding the optimum output differences, given the two input differences and the optimum output masks, given the two input masks for the operation of modular addition mod 2n, the process of finding good linear and differential characteristics for the lightweight ciphers SIMON and SPECK could be sped up, and the complexity of linear and differential attacks against these ciphers could be reduced

Summary

Introduction

SIMON and SPECK are two families of block ciphers that were designed by the NSA [1]. These lightweight ciphers have widely attracted the attention of researchers [2,3,4,5,6,7,8,9,10,11,12,13,14]. By the aid of the main contribution of the current paper, i.e., the full description of DDT and LAT of φ, which in turn leads to the full determination of DDT and LAT of the core quadratic mapping of SIMON, as well as the straightforward algorithms for finding the optimum output differences, given the two input differences and the optimum output masks, given the two input masks for the operation of modular addition mod 2n , the process of finding good linear and differential characteristics for the lightweight ciphers SIMON and SPECK could be sped up, and the complexity of linear and differential attacks against these ciphers could be reduced.

Preliminary Notations and Definitions

Linear and Differential Properties of SIMON

Linear and Differential Properties of SPECK

Conclusions