I am wondering: If we take this scheme/procedure and each of it seems very secure (to me at least), is it truly secure or is there a vulnerability hidden in the process?
This is the scheme:
Bob has an RSA key with modulo $N$ with a size that is considered safe, 2048 and a public power of $e=3$ (should assure efficient encryption).
Alice wants to send Bob a big file, and chooses symmetric encryption: She uses a random $k$ for AES and sends it encrypted using RSA using $C=k^e \bmod N$, and then sends the file encrypted by AES using key $k$.
To decrypt the file, Bob recovers $k$ using $k=C^d \bmod N$ and then decrypts the encrypted file using AES with $k$ is the key.
Is this procedure really secure?
On the paper, it uses secure parameters and seems secure, but I am not sure because $k$ is used too much here. Is there some hidden vulnerability I am missing here?
EDIT: what i am asking is in regards to attacking it, so could you please put an emphasize on attacking it rather than suggesting an alternative? i don't fully understand it, i understand that because of AES, $k^3$ cannot be more than 768 bits, so it does not pass the modulo (that is 2048). but i don't understand the technical details very well and would appreciate if you could elaborate on it instead of on possible mitigations.
thank you very much