Truncated differential characteristics with minimum number of active bytes for simplified Whirlpool

In this paper, a truncated differential characteristics with minimum number of active bytes is built to produce a collision for two reduced variants of the hash function Whirlpool: with 1 and 2 rounds in the underlying block-cypher instead of 14. For the first variant this number equals 23, for the second one – 45. The probabilities of these characteristics are maximal and equal $2^{-115}$ and $2^{-225}$ respectively.