RSA: Large public key exponent support?

Vault
1

I’ve ran into an issue with RSA that surprised me. I’ve noticed an error coming from Hashicorp Vault when trying to sign a CSR created with a large public key exponent (0x100000001). I’ve been going through the documentation and consulted few colleagues but didn’t get any answers. The largest possible value I tested that works is 0x10000001.

I’ve searched for a similar topic here and on GitHub but did not find anything. Is this even a valid use-case? I’m not well-versed in cryptography: maybe such exponent value is invalid? Is this limitation documented anywhere or am I just all wrong and confused here? :slight_smile:

Here’s how I create the key pair for testing:

$ openssl req -sha256 \
  -newkey rsa:4096 -noenc \
  -pkeyopt rsa_keygen_pubexp:0x100000001