Nano LANReach Internet Protocols:
• ARP, ICMP, IP, UDP, TCP, DHCP, DNS, NTP, SMTP, POP3, MIME, HTTP, FTP and TELNET
• Security protocols: SSL3/TLS1, HTTPS, FTPS, RSA, AES-128/256, 3DES, RC-4, SHA-1, MD-5
• Protocols accelerated in hardware: AES, 3DES and SHA

I'm not a security expert but those specs look good.

It has a web server (current versions are 64KB, later versions will be bigger).

It can be configured to check a Network Time Sever at power-up and every four hours thereafter.

It's easy to program, using a variant on AT commands.

All in all it exceeds my fondest hopes for an embedded ethernet interface. The low price may due to the current high value of the dollar. It's available from Mouser and others.