The research of block ciphers non-injective key schedules properties

Abstract

The considers non-injective key schedules used in many known block ciphers ("Kalyna", FOX, Twofish, etc.). It is estimated the probability of matching of round keys (formed by non-injective key schedule) set and encryption keys set cardinalities; a theorem which determines such a probability is formulated and proved. It is shown that for a full cipher with a non-injective key schedule, the probability of matching of round keys set and encryption keys set cardinalities is practically equal to 1. Thus, it is proved that the exhaustive search attacks complexity on non-injective key schedules is almost equal to injective ones (the exhaustive search attacks complexity does not decrease). At the same time, non-injective key schedules provide additional strength to attacks on the implementation and other attacks.