Paper 2026/756

Integral Attack on Reduced-Round Kalyna

Abstract

We study integral cryptanalysis of the Ukrainian block cipher Kalyna and focus on constructing reduced-round distinguishers and key-recovery attacks with low data, time, and memory complexities. Although Kalyna has an SPN-type round structure, its pre-whitening and post-whitening layers use column-wise addition modulo $2^{64}$, which makes the propagation of integral properties more delicate than in XOR-only designs. By combining carefully chosen input multisets with backward extension through inverse round transformations, we obtain integral distinguishers for Kalyna-128, Kalyna-256, and Kalyna-512 in the standard setting, under weak-key assumptions, and in variants without pre-whitening. These distinguishers require as few as $2^8$ or $2^{16}$ chosen texts, substantially improving the data complexity of previously reported public integral results on Kalyna. We further extend them to key-recovery attacks on reduced-round Kalyna by partial decryption and balancedness tests on suitable intermediate states. For example, we obtain a $5$-round key-recovery attack on Kalyna-128/128 with data complexity $2^9$ chosen plaintexts, time complexity $2^{74}$ encryptions, and negligible memory. To the best of our knowledge, this is the first work to provide integral cryptanalysis of Kalyna-256/256 and Kalyna-512/512. Overall, our results give a unified integral analysis of Kalyna across its standard block sizes and clarify the effect of modular whitening on reduced-round distinguishers and key-recovery attacks.