Security implications of leaking d, e, and a ciphertext in an RSA calculation?

silent-cartographer

3/20/24, 10:03 AM

I'm learning about RSA, and one of the textbooks I'm studying from talks about the security implications of various parts of an RSA key pair being leaked. It talks about what happens when an attacker knowns only n and e, only n and d, etc.

One of the combinations it did not cover was one that I was thinking about: what happens when an attacker knows only d, e, and tries to decrypt a given ciphertext c? If p and q are 128 bit primes used in generating n, (all 3 of which are unknown to the attacker#, is it feasible for the attacker to derive n, and then use this knowledge to break a ciphertext? Is there a more effective to way simply use the half of the private key (d), and the half of the public key you do have (n), to attack and derive the plaintext, without calculating n directly, which I would assume would require a lot of computation?

0 + 1

fgrieu

3/20/24, 10:35 AM

Duplicate of this [recent question](https://crypto.stackexchange.com/q/105734/555). There is now little doubt this is a thinly disguised CTF, homework or similar. No matter how interesting and fun, this is off-topic. [update] Ah it's [admitted it's a CTF](https://crypto.stackexchange.com/posts/comments/226368), and we are told it's finished.

Elon Musk

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