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Let's Encrypt manual ECDSA certificate signing request
EDIT 2022: certbot
v1.10 onwards does automate EC cert creation with a config change
Just the bare essentials below (with my own modifications):
openssl ecparam -genkey -name secp384r1 | openssl ec -out ec.key
openssl req -new -sha256 -key ec.key -nodes -out ec.csr -outform pem
Depending on certbots ACME challenge methods preferred:
certbot certonly \
--dns-cloudflare --dns-cloudflare-credentials cloudflare_id.ini \
-d h.auyong.me --csr ./ec.csr
certbot certonly -w /var/www/ayhx/_site/ -d h.auyong.me --csr ./ec.csr
Source: Using ECDSA certificates with Let's Encrypt, 2016