Cryptology ePrint Archive: Report 2020/005

Lai-Massey Scheme Revisited

M. R. Mirzaee Shamsabad and S. M. Dehnavi

Abstract: Lai-Massey scheme is a well-known block cipher structure which has been used in the design of the ciphers PES, IDEA, WIDEA, FOX and MESH. Recently, the lightweight block cipher FLY applied this structure in the construction of a lightweight $8 \times 8$ S-box from $4 \times 4$ ones. In the current paper, firstly we investigate the linear, differential and algebraic properties of the general form of S-boxes used in FLY, mathematically. Then, based on this study, a new cipher structure is proposed which we call generalized Lai-Massey scheme or GLM. We give upper bounds for the maximum average differential probability (MADP) and maximum average linear hull (MALH) of GLM and after examination of impossible differentials and zero-correlations of one round of this structure, we show that two rounds of GLM do not have any structural impossible differentials or zero-correlations. As a measure of structural security, we prove the pseudo-randomness of GLM by the H-coefficient method.

Category / Keywords: secret-key cryptography / Generalized Lai-Massey Scheme; S-box; Symmetric Cipher; H-coefficient Method; MADP; MALH.

Date: received 2 Jan 2020, last revised 2 Jan 2020

Contact author: std_dehnavism at khu ac ir

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Version: 20200103:074218 (All versions of this report)

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