[exim] DKIM ed25519 signing issues

I have successfully set up DKIM using rsa keys, but am having issues
with ed25519 keys.
Using an ed25519 key I get
DKIM: signing failed: RSA_PRIVKEY
in the exim log. As I said, RSA key works.

I have tried generating the key with both ssh-keygen and with certtool,
as follows:
ssh-keygen -t ed25519 -f foo.privkey
certtool --generate-privkey --key-type=ed25519 --outfile=foo.privkey

I need to use ed25519 keys to keep the size of the public key small
(required by the BT domain manager tool for TXT records).

Has anyone successfully used Exim and DKIM with ed25519 keys? Any pointers?