Larger RSA keys (Modulus bits > 16384)

Grégory Widmer gregory.widmer at
Sun Dec 26 15:21:48 UTC 2021

Dear OpenSSL users,

I have a question about OpenSSL. Recently, I asked myself if there was a 
maximum bit length for the modulus of a RSA key.

I tried to type :

user at host:~$ openssl genrsa 32768
Warning: It is not recommended to use more than 16384 bit for RSA keys.
          Your key size is 32768! Larger key size may behave not as 
Generating RSA private key, 32768 bit long modulus (2 primes)

I got this warning, and I wonder why a larger key size may behave not as 

Could anyone explain or give resources on why this doesn't work ?

My guess is that, having the following : (M = message, C = Ciphered)

If M^e is < n, we could easily compute the original message ?

Also, I want to apologize if my question is redundant, I tried to search 
on GitHub and through the mailing list, but there is no search feature 
in the mailing list.

Have a nice day !

Grégory Widmer

PS : This question is for knowledge purpose only, I don't use RSA keys 
anymore (except with GPG), I prefer ECC :)

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