Authentication across sites

[vast55555]

Hello,

I've been reading old posts and articles but haven't found a solution
yet for the following.

I'd like to authenticate users across two different sites on two
different domains--in other words, a single sign-on scheme--so once the
user has logged into Site 1, we can transfer his login or session to
Site 2.

The first site isn't .NET and isn't running under the same domain so I
can't use Forms Authentication with the same machine key as suggested
in other posts. I think we'll still need to do something on their end
using whatever (non-.NET) scripting technology they have available, and
we should be able to accomplish this.

One thought is to store usernames and encrypted passwords in our
database, and have Site 1 pass us these data (from a posted form,
perhaps?) for authentication, possibly over SSL. Our preference,
though, is not to have any login data--encrypted or otherwise--in our
possession.

Or something using Web services?

I haven't had to deal with this before so I'm a bit stumped on this
one. Thanks!