In examining these other accounts, agents uncovered sexually
explicit e-mails that Broadwell exchanged with another party who
also used a Gmail account. Investigators were not able to
immediately identify Petraeus as the other party, however, because
he’d set up his Gmail account using a pseudonym.
Investigators determined sometime during mid-summer that it
belonged to Petraeus and that the two were having an affair. The
reports do not say how investigators made that connection.
According to the New York Times it’s not known if the FBI gained
access to Petraeus’ personal e-mail account, or if its
investigation relied solely on e-mails found in Broadwell’s
Google, which offers e-mail, cloud storage, a blogging platform,
web search, and other services, provides government agencies with
e-mail communications, documents, browsing activity, IP addresses
used to create an account and other data when asked.
I find it almost shocking that the director of the CIA would be foolish enough to think that a pseudonymous Google account was safe enough to exchange email with his mistress.