Explore a groundbreaking paper on impossible differential cryptanalysis presented at Eurocrypt 2017. Delve into the new search tool developed by Yu Sasaki and Yosuke Todo, examining its design and cryptanalytic applications. Learn about the fundamentals of impossible differential attacks, their history, and the general methods employed. Understand the model block cipher, impossible-to-financial strength, and type structure. Examine the extended facial network, impossible differential assumptions, and a practical example. Conclude with insights on linear key schedules and the implications for modern cryptography.