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Given that this data breach included highly personal information that many of the members might not want shared, it’s alarming to think that a thief could extort money from some of the members in exchange for not blasting the news of their participation in a site dedicated to sexual relationships with strangers.This practice has unfortunately become so commonplace in the world of social media that it has its own term, sextortion.
Physical addresses can lead to mail fraud and “dumpster diving,” which can then easily turn into other potential forms of identity theft, scams, or fraud.
Gmail (or equivalent - there are many other free online mail providers) gives you a full blown email address and obviously requests a lot of info in the process.
A great alternative where an email address is simply a requirement to entry and you care little about anything that's actually sent to it is to use a Mailinator address.
The email address is the first, most logical step and honestly this is a huge portion of the anonymity story as it relates to identities being spread around the web when a system is compromised. Consider the data that many sites request on signup: name, location (possibly your exact address), date of birth, phone number etc.
If protecting your identity is indeed important to you, consider what these values should be.