tl;dr:1. Start with `e*d == 1 mod phi(N)` and thus `e*d - k*phi(N) == 1`2. Notice that `e*d0 - k*phi(N) == 1 mod 2**1050`3. Using the definition of `phi` for given 4 public keys formulate equation with a single variable and solve it to recover prime factors
Full writeup: https://github.com/p4-team/ctf/tree/master/2019-09-21-dragonctf/rsachained