Earlier quoted context omitted.
You don't even need (3) if you can do enough trials and have an accurate clock. Compression by its very nature drips timing side channels.
Due to the padding of even compressed SSL segments only having timing data will significantly complicate things. You'll be trying to measure the variance in deflate compressing different blocks with single byte differences. You better have an extremely low jitter connection!
Like AWS. (Cite: http://dl.acm.org/citation.cfm?id=1653687.)