About a month after Google launched encrypted search at https://www.google.com/, they will be moving it to https://encrypted.google.com/.
The reason for the move is due to “better serve our school partners and their users,” said Dave Girouard, President, Google Enterprise. The issue with having it at https://www.google.com/ is that they can block encrypted searches via their network without it impacting services such as Google Apps for Education. For example, most Google Apps products require authentication through https://www.google.com/ and if an administrator wanted to just block the SSL version of Google web search they would ultimately have to block that authentication as well.
Moving this to it’s own subdomain gives administrators a way to just block Google’s SSL search.