Weak-Key Classes and Key Recovery in Key-Then-Hash Functions

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Handschuh and Preneel define a weak-key class by “unexpected” security behavior and efficient detection of class membership. Four families in their CRYPTO 2008 analysis, NH, NMH, WH, and Square Hash, fall within the later key-then-hash (KTH) formalism. For the controlled collision and fixed-difference attacks considered here, KTH offset-invariance shows that any nonempty solution set can be translated to contain any chosen absolute key while preserving its size, success probability, and the numb