Weak RSA Senario

RSA is a public key crypto algorithm that relies on the difficulty of factoring large primes. Modern RSA uses at least $1024$ bit keys, and up to $16384$ bit keys for SSH $($that$\text{'}$s a bit extreme, usually around $4096$ is used for high security.$)$

Other encryption standards that do not rely on prime number factorization require much smaller key sizes. For example, AES $($a symmetric algorithm$)$ can be extremely secure with just $256$ bits, or Elliptic Curve public key crypto, which can be unbreakable enough with just $224$ bits.

Because encryption with RSA is slow and $($computationally$)$ expensive, it is usually done by encrypting a symmetric key $($such as AES$),$ and encrypting the actual data with symmetric cryptography instead. That is how TLS and HTTPS works.

But what happens when the RSA key is a bit too small? Break the RSA pub key below to get the private key, and then decrypt the secret which is encrypted via the symmetric key.