New Division Property Propagation Table: Applications to Block Ciphers with Large S-boxes. (13th February 2021)

• Record Type: Journal Article
• Authors: Hu, Xichao; Li, Yongqiang; Jiao, Lin; Wang, Mingsheng
• Is Part Of: Computer journal. Volume 65:Number 6(2022)
• Page Start: 1560
• Page End: 1573
• Publication Date: 2021-02-13
• Subjects: bit-based division property -- mixed-integer linear programming (MILP) -- integral distinguishers -- large S-boxes; Computers -- Periodicals; 005.1
• DOI: 10.1093/comjnl/bxaa203
• Languages: English
• ISSNs: 0010-4620

Abstract

Abstract: The division property method is a technique for automatic searching integral distinguishers on block ciphers. Previous methods only use word-based division property to search integral distinguishers for block ciphers with large S-boxes. Since using bit-based division property may find longer integral distinguishers than word-based division property, we propose a method to automatically search the integral distinguishers based on bit-based division property for block ciphers with large S-boxes. To achieve this goal, we propose a new division property propagation table for S-boxes. Theoretically, we prove that using both the new table and the traditional method to describe the bit-based division property propagation rule of S-box will lead to the same integral distinguishers. Technically, we design a mixed-integer linear programming-based tool to search the integral distinguisher based on the new table, which helps to search new integral distinguishers for block ciphers with large S-boxes efficiently. As a result, we apply our tool to derive new integral distinguishers and get the tight bound on the rounds that no integral distinguishers exist for ICEBERG, KHAZAD, Camellia, CS-Cipher, ITUbee and SMS4. Besides, to show the availability of our integral distinguishers, we form the present best five-round and the first six-round integral attack for ICEBERG as an example.