Cryptology ePrint Archive: Report 2016/036

Characterizations of the Degraded Boolean Function and Cryptanalysis of the SAFER Family

wentan Yi and Shaozhen Chen

Abstract: This paper investigates the degradation properties of Boolean functions from the aspects of the distributions of di erences and linear masks, and shows two characterizations of the degraded Boolean function. One is that there exists a linear space of the input di erences, where the di erentials with the zero output di erence have probability 1; Another one is that the input linear masks of the nonzero-correlation linear approximations are included in a linear space. Those two linear spaces are orthogonal spaces. Moreover, the degradation properties are showed about the exponentiation type S-box of the SAFER block ciphers, which are applied to reduce the compute complexity in the zero-correlation linear attacks on 5-round SAFER SK/128, 4(5)-round SAFER+/128(256) and 5(6)-round SAFER++/128(256). In the attacks, some of the linear properties of PHT employed as the linear layer by the SAFER block ciphers are investigated and some zero-correlation approximations for SAFER SK, SAFER+, and SAFER++ are identi ed, when only the least one or two signi cant bits are considered. The results show that more rounds of some of the SAFER block ciphers can be attacked, by considering the degradation properties and the zero-correlation linear relations.

Category / Keywords: secret-key cryptography / Cryptography / Block cipher / Degradation property / Zero- correlation linear cryptanalysis / SAFER

Date: received 13 Jan 2016

Contact author: nlwt8988 at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20160114:014231 (All versions of this report)

Short URL: ia.cr/2016/036

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