Division property
A generalisation of the integral attack's balance properties that tracks which algebraic degrees survive through a cipher's rounds.
Yosuke Todo introduced the division property at Eurocrypt 2015. Classic integral cryptanalysis tracks whether a set of values is constant, balanced or unknown; Todo's formalism instead tracks which monomials of the plaintext bits can still appear after each round. That yields longer distinguishers. The same year he used it to break full MISTY1, a cipher that had held up since the 1990s and whose descendant KASUMI encrypts 3G traffic.
The bit-based variant is far too expensive to work out by hand, so researchers now translate its propagation rules into mixed-integer linear programs and let a solver do the searching. It has since powered cube attacks on Trivium and is a standard tool whenever a new lightweight cipher gets scrutinised.