SSL, Gone in 30 seconds
breachattack.com
breachattack.com
What you want to know about BREACH is that it's an application of Thai Duong and Juliano Rizzo's extremely clever CRIME attack, a traffic-analytic side channel based on compression and attacker chosen plaintext, but instead of targeting compression at the TLS layer, it targets Content-encoding: gzip.
Unlike CRIME, BREACH can't directly target cookies, which is usually what an attacker targeting HTTPS/TLS is aiming for; BREACH can only decrypt secrets in the response body. A common example people have tossed around is CSRF tokens.
One example might be to decipher a bank statement page. First the tool would guess the first section of dynamic content (account balance), then the second (account name), then the third (account number), etc. Though I imagine banks already have some rate limiting protection in place.
BREACH is far more insidious, because there is no "easy" solution for many people. Disabling HTTP compression is a huge performance hit. The alternative is auditing every single endpoint to ensure that it won't leak attacker data into the response, which is practically an impossible proposition.
Sure, attackers have to do a bit more work to identify a vulnerable endpoint. But developers have to do exponentially more work locking down all exposed parts of their application. Not really a good tradeoff IMO.
EDIT: there's the added bonus that BREACH stomps all over the ideal "isolation" between crypto and application code. In fact, BREACH may indicate that such isolation is inherently impossible: you can't write safe application code without knowledge of the crypto you're running on.
EDIT 2: s/daunting/impossible/
I think you're underestimating how common this is.
For example, view source on https://www.google.com/search?q=pajamas and look at how many times "pajamas" appears on the page.
This is a simple example, but query string parameters (and other attacker-controlled data) get reflected in server responses all the time. Eliminating this behavior is not a realistic goal.
The mitigation suggestions are all at the application level which will make fixes less likely as SSL/TLS is usually considered a security silver bullet.
Adding a fixed amount of random bytes will have no benefit at all.