Multidimensional Meet-in-the-Middle Attack and Its Applications to GOST, KTANTAN and Hummingbird-2
This paper investigates a new approach to analyze symmetric ciphers by dividing the algorithms to consecutive sub-ciphers and then evaluating them separately. This attack is suitable for ciphers with simple key schedules and having block sizes smaller than key lengths. The authors have successfully applied this multidimensional approach to the block ciphers, GOST and KTANTAN32/48/64, and found attacks with time complexities less than all existing results. An attack on full Hummingbird-2 faster than exhaustive search but requiring large memory is also constructed by using this method.