In this study, the authors present some new algorithms for the unbalanced generalised birthday problem (UGBP), which was proposed by Nikolić and Sasaki in their attacks on the generalised birthday problem (GBP). The authors’ first idea is simple, which uses some precomputing to convert UGBP into GBP. After the precomputing, they just adopt Wagner's k ‐tree algorithm or the algorithms of Bernstein et al . to solve UGBP. Their second idea combines the technique for the unbalanced meet‐in‐the‐middle problem with the improved time–memory trade‐off algorithm for GBP to solve UGBP. Besides, they will utilise the inactive technique and the rearrangement technique to improve the time complexities of their algorithms. The inactive technique is used to neglect the effect of some costly functions, and the rearrangement technique is adopted to balance the time costs between different functions. When k is not a power of 2, the time complexity of their algorithms for UGBP can also be improved by using the multicollision technique.

Generalised Feistel network (GFN) is a popular design for block ciphers and hash functions. The round function of the network often chooses a substitution–permutation (SP) transformation (consists of a subkey XOR, an S‐boxes layer and a linear layer). In 2011, Bogdanov and Shibutani provided another choice to build round functions, namely the double SP‐functions, which has two SP‐layers in series. They showed that a 4‐branch type‐2 GFN with double SP‐functions was stronger than the one with single SP‐function in terms of the number of active S‐boxes in a differential or linear cryptanalysis, but some subsequent results showed that the double SP‐function is the weaker one in some known‐key scenarios and hashing modes. In this study, the authors present a new result of the 4‐branch type‐2 GFN, whose round function is a single SP‐function. They show some 15‐round truncated differential distinguishers for this network with four usual parameters by utilising some rebound attack techniques. Based on these distinguishers, they construct some 15‐round near‐collision attacks on the Matyas–Meyer–Oseas and Miyaguchi–Preneel compression function modes in which the 4‐branch type‐2 GFN with the single SP‐function is used.