From the link that was posted in reply to you, 'hope against hope' means 'to have hope even when the situation appears to be hopeless'. Which means he does have hope, even though the situation appears to be hopeless.
Why is the situation hopeless? Google, for example, has been undertaking efforts for years to improve security on the Internet, in part for the purpose of protecting privacy. Seven days ago they were featured in an article about how they're going to warn users of Gmail whose incoming emails are not protected by SSL: https://news.ycombinator.com/item?id=11067050 - this is part of their Safer Email initiative. Some time ago they released a Transparency Report as part of that initiative describing which senders to/from Gmail support encryption: https://www.google.com/transparencyreport/saferemail/ - and that's not to mention their efforts promoting HTTPS.
I see these efforts as Google going far out of its way to support privacy and security on the web.
[1] - http://idioms.thefreedictionary.com/hope+against+hope