Hi Nicolas,
ASA support TLS 1.2 in 9.3(x) which is not available for ASA 5510.
As per below discussion, it doesn't seem that it would be added for ASA 5510.
https://supportforums.cisco.com/discussion/11737801/tls-12-asa-clientless-ssl-vpn
ASA 5510 is EOL so it doesn't look likely that there would addition of any feature on it.
From EOL notice:
The Cisco ASA 9.1 is the last software release that will be supported on ASA 5510 and other ASA 5500 appliances that have reached their end-of-sale date.
http://www.cisco.com/c/en/us/products/collateral/security/asa-5500-series-next-generation-firewalls/eol_C51-727283.html
Regards,
Kanwal
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