- Category: Reversing
- Score: 482/500
- Solves: 15
All you need is to make it compile without error!
A lot of the types are defined using tail recursion, and it is easy to see it defines things like how strings are encoded into integers, arithmetic in GF(67) and matrix multiplication. In a nutshell, there are two constant 8x8 matrices A and B and the flag is converted into a 8x8 matrix X. The flag has length 62, so the missing part will be converted to undefined, which is same as 0. To pass the check, X must satisfy A*X=X*B (mod 67).
By flattening the A*X-X*B=0 (mod 67) equations you will get a linear system of 64 unknowns and 64 equations, so gaussian elimination will solve the problem. The system is actually linear (not affine), so the solution will be in a kernel of a matrix. But if you investigate furture you will find the rank of the system is 8*8-8=60, so the kernel dimension is 8, this means there are a lot of valid X that satisfty A*X=X*B. Combining this with the flag format and the fact that flag has length 62, you can eliminate 8 unknowns and get the only possible solution, which is the flag.