- a public key $(n,e)$ where modulus $n$ has 615 decimal digits.
- a decryption exponent $d$ with 8 decimal digits currupted with known positions.
- a plaintext-ciphertext pair $c_1 = m_1^e \bmod n$
- just a ciphertext c_2 encrypted with the public key $(n,e)$
I want to decrypt $c_2$.
I'm sorta lost on what I can do with these information. My main focus is trying to get D1. It is 615 char. long, with 8 digits randomly missing throughout it. Trying to bruteforce it would be going through 10$^8$ possibilities. Even if I can somehow do that, what would I even do with all of them? decrypt the ciphertext and see which D1 matches the plaintext? I dont know if that possible on a laptop.
I tried computing the euler phi function of N, but being a large number, I dont know if i can compute it. I had it running for 20min before I interrupted the calculation.
What else can I do with all this information?