Cryptology ePrint Archive: Report 2017/1211

Zero-Sum Partitions of PHOTON Permutations

Qingju Wang and Lorenzo Grassi and Christian Rechberger

Abstract: We describe an approach to zero-sum partitions using Todo’s division property at EUROCRYPT 2015. It follows the inside-out methodology, and includes MILP-assisted search for the forward and backward trails, and subspace approach to connect those two trails that is less restrictive than commonly done.

As an application we choose PHOTON, a family of sponge-like hash function proposals that was recently standardized by ISO. With respect to the security claims made by the designers, we for the first time show zero-sum partitions for almost all of those full 12-round permutation variants that use a 4-bit S-Box. As with essentially any other zero-sum property in the literature, also here the gap between a generic attack and the shortcut is small.

Category / Keywords: PHOTON, Integral, Division Property, Zero-sum, MILP, Subspace

Original Publication (with minor differences): CT-RSA 2018

Date: received 18 Dec 2017, last revised 7 Mar 2018

Contact author: lorenzo grassi at iaik tugraz at

Available format(s): PDF | BibTeX Citation

Version: 20180307:151726 (All versions of this report)

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