Larger RSA keys (Modulus bits > 16384)

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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@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 expected.
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 expected.

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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