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First, let's go over how cipher suite negotiation works, very briefly. For example, we can use the TLS 1.2 document RFC 5246 starting at section 7.4.1.2 to see, in the short short form:

First, let's go over how cipher suite negotiation works, very briefly. For example, we can use the TLS 1.2 document RFC 5246 starting at section 7.4.1.2 to see, in the short short form:

Essentially, you need to tell Nginx to use the order you select, and you need to select an order. To see what the results of that order would be, you can use the OpenSSL command line, i.e.

openssl ciphers -v EECDH+ECDSA+AESGCM:EECDH+aRSA+AESGCM:EECDH+ECDSA+SHA256:EECDH+aRSA+SHA256:EECDH+ECDSA+SHA384:EECDH+ECDSA+SHA256:EECDH+aRSA+SHA384:EDH+aRSA+AESGCM:EDH+aRSA+SHA256:EDH+aRSA:EECDH:!aNULL:!eNULL:!MEDIUM:!LOW:!3DES:!MD5:!EXP:!PSK:!SRP:!DSS:!RC4:!SEED

Essentially, you need to tell Nginx to use the order you select, and you need to select an order. To see what the results of that order would be, you can use the OpenSSL command line, e.g.

openssl ciphers -v 'EECDH+ECDSA+AESGCM:EECDH+aRSA+AESGCM:EECDH+ECDSA+SHA256:EECDH+aRSA+SHA256:EECDH+ECDSA+SHA384:EECDH+ECDSA+SHA256:EECDH+aRSA+SHA384:EDH+aRSA+AESGCM:EDH+aRSA+SHA256:EDH+aRSA:EECDH:!aNULL:!eNULL:!MEDIUM:!LOW:!3DES:!MD5:!EXP:!PSK:!SRP:!DSS:!RC4:!SEED'

Edited to add: At least after this (if not before also), go to Qualys SSL Labs to see HTTPS security information and to Test Your Server that's been kept pretty well up to date for the last few years. Recommendations change regularly, and sometimes even frequently reverse themselves (RC4, for example, what nearly whiplash inducing). You can also even Test Your Browser!