Hello.
I am running Nginx 1.21.6 with OpenSSL 3.0.1 and the Mozilla [1] 'Modern' ciphers 4.0 without issue. When I change the ciphers to Mozilla 'modern' 5.5, Nginx fails a config test with:

nginx: [emerg] SSL_CTX_set_cipher_list("TLS_AES_128_GCM_SHA256:TLS_AES_256_GCM_SHA384:TLS_CHACHA20_POLY1305_SHA256") failed (SSL: error:0A0000B9:SSL routines::no cipher match).

The line in nginx.conf with 'Modern' 5.5 ciphers (fails test) is:

ssl_ciphers 'TLS_AES_128_GCM_SHA256:TLS_AES_256_GCM_SHA384:TLS_CHACHA20_POLY1305_SHA256';

The line in nginx.conf with 'Modern' 4.0 ciphers (passes test) is:

ssl_ciphers 'ECDHE-ECDSA-AES256-GCM-SHA384:ECDHE-RSA-AES256-GCM-SHA384:ECDHE-ECDSA-CHACHA20-POLY1305:ECDHE-RSA-CHACHA20-POLY1305:ECDHE-ECDSA-AES128-GCM-SHA256:ECDHE-RSA-AES128-GCM-SHA256:ECDHE-ECDSA-AES256-SHA384:ECDHE-RSA-AES256-SHA384:ECDHE-ECDSA-AES128-SHA256:ECDHE-RSA-AES128-SHA256';

At compile time, I used the `--with-openssl` flag to point to the Nginx-specific OpenSSL, which I confirm is 3.0.1:

$ sudo /etc/nginx/openssl/bin/openssl version
OpenSSL 3.0.1 14 Dec 2021 (Library: OpenSSL 3.0.1 14 Dec 2021)

That instance of OpenSSL has the following ciphers:

$ sudo /etc/nginx/openssl/bin/openssl ciphers
TLS_AES_256_GCM_SHA384:TLS_CHACHA20_POLY1305_SHA256:TLS_AES_128_GCM_SHA256:ECDHE-ECDSA-AES256-GCM-SHA384:ECDHE-RSA-AES256-GCM-SHA384:DHE-RSA-AES256-GCM-SHA384:ECDHE-ECDSA-CHACHA20-POLY1305:ECDHE-RSA-CHACHA20-POLY1305:DHE-RSA-CHACHA20-POLY1305:ECDHE-ECDSA-AES128-GCM-SHA256:ECDHE-RSA-AES128-GCM-SHA256:DHE-RSA-AES128-GCM-SHA256:ECDHE-ECDSA-AES256-SHA384:ECDHE-RSA-AES256-SHA384:DHE-RSA-AES256-SHA256:ECDHE-ECDSA-AES128-SHA256:ECDHE-RSA-AES128-SHA256:DHE-RSA-AES128-SHA256:ECDHE-ECDSA-AES256-SHA:ECDHE-RSA-AES256-SHA:DHE-RSA-AES256-SHA:ECDHE-ECDSA-AES128-SHA:ECDHE-RSA-AES128-SHA:DHE-RSA-AES128-SHA:RSA-PSK-AES256-GCM-SHA384:DHE-PSK-AES256-GCM-SHA384:RSA-PSK-CHACHA20-POLY1305:DHE-PSK-CHACHA20-POLY1305:ECDHE-PSK-CHACHA20-POLY1305:AES256-GCM-SHA384:PSK-AES256-GCM-SHA384:PSK-CHACHA20-POLY1305:RSA-PSK-AES128-GCM-SHA256:DHE-PSK-AES128-GCM-SHA256:AES128-GCM-SHA256:PSK-AES128-GCM-SHA256:AES256-SHA256:AES128-SHA256:ECDHE-PSK-AES256-CBC-SHA384:ECDHE-PSK-AES256-CBC-SHA:SRP-RSA-AES-256-CBC-SHA:SRP-AES-256-CBC-SHA:RSA-PSK-AES256-CBC-SHA384:DHE-PSK-AES256-CBC-SHA384:RSA-PSK-AES256-CBC-SHA:DHE-PSK-AES256-CBC-SHA:AES256-SHA:PSK-AES256-CBC-SHA384:PSK-AES256-CBC-SHA:ECDHE-PSK-AES128-CBC-SHA256:ECDHE-PSK-AES128-CBC-SHA:SRP-RSA-AES-128-CBC-SHA:SRP-AES-128-CBC-SHA:RSA-PSK-AES128-CBC-SHA256:DHE-PSK-AES128-CBC-SHA256:RSA-PSK-AES128-CBC-SHA:DHE-PSK-AES128-CBC-SHA:AES128-SHA:PSK-AES128-CBC-SHA256:PSK-AES128-CBC-SHA

The three ciphers used in Mozilla 'Modern' 5.5 are "TLS_AES_128_GCM_SHA256:TLS_AES_256_GCM_SHA384:TLS_CHACHA20_POLY1305_SHA256", which happen to be the first three ciphers in the long list above. it follows that OpenSSL 3.0.1 has support for these three ciphers, and the naming convention matches.

I am unsure why Nginx shows the error relating to "no cipher match" when the ciphers are present in the TLS library.

The system-native OpenSSL includes those ciphers, too (again, first three in the list of ciphers):

$ openssl version
OpenSSL 1.1.1f 31 Mar 2020
$ openssl ciphers
TLS_AES_256_GCM_SHA384:TLS_CHACHA20_POLY1305_SHA256:TLS_AES_128_GCM_SHA256:ECDHE-ECDSA-AES256-GCM-SHA384:ECDHE-RSA-AES256-GCM-SHA384:DHE-RSA-AES256-GCM-SHA384:ECDHE-ECDSA-CHACHA20-POLY1305:ECDHE-RSA-CHACHA20-POLY1305:DHE-RSA-CHACHA20-POLY1305:ECDHE-ECDSA-AES128-GCM-SHA256:ECDHE-RSA-AES128-GCM-SHA256:DHE-RSA-AES128-GCM-SHA256:ECDHE-ECDSA-AES256-SHA384:ECDHE-RSA-AES256-SHA384:DHE-RSA-AES256-SHA256:ECDHE-ECDSA-AES128-SHA256:ECDHE-RSA-AES128-SHA256:DHE-RSA-AES128-SHA256:ECDHE-ECDSA-AES256-SHA:ECDHE-RSA-AES256-SHA:DHE-RSA-AES256-SHA:ECDHE-ECDSA-AES128-SHA:ECDHE-RSA-AES128-SHA:DHE-RSA-AES128-SHA:RSA-PSK-AES256-GCM-SHA384:DHE-PSK-AES256-GCM-SHA384:RSA-PSK-CHACHA20-POLY1305:DHE-PSK-CHACHA20-POLY1305:ECDHE-PSK-CHACHA20-POLY1305:AES256-GCM-SHA384:PSK-AES256-GCM-SHA384:PSK-CHACHA20-POLY1305:RSA-PSK-AES128-GCM-SHA256:DHE-PSK-AES128-GCM-SHA256:AES128-GCM-SHA256:PSK-AES128-GCM-SHA256:AES256-SHA256:AES128-SHA256:ECDHE-PSK-AES256-CBC-SHA384:ECDHE-PSK-AES256-CBC-SHA:SRP-RSA-AES-256-CBC-SHA:SRP-AES-256-CBC-SHA:RSA-PSK-AES256-CBC-SHA384:DHE-PSK-AES256-CBC-SHA384:RSA-PSK-AES256-CBC-SHA:DHE-PSK-AES256-CBC-SHA:AES256-SHA:PSK-AES256-CBC-SHA384:PSK-AES256-CBC-SHA:ECDHE-PSK-AES128-CBC-SHA256:ECDHE-PSK-AES128-CBC-SHA:SRP-RSA-AES-128-CBC-SHA:SRP-AES-128-CBC-SHA:RSA-PSK-AES128-CBC-SHA256:DHE-PSK-AES128-CBC-SHA256:RSA-PSK-AES128-CBC-SHA:DHE-PSK-AES128-CBC-SHA:AES128-SHA:PSK-AES128-CBC-SHA256:PSK-AES128-CBC-SHA

I would be grateful for any advice on what I am doing wrong here, especially for further reading where I can better understand any missteps.

I appreciate this is a wall-of-text email, I've tried my best to split it up sensibly.

Thank you for reading, and thank you for your time & expertise.

[1] https://wiki.mozilla.org/Security/Server_Side_TLS