Depending on your meaning, this may not be a workable system. There are three different types of factors that can be used for authentication, what you have, who you are and what you know.
What You Know
For what you know, your constraint is that it can only use publicly available information. This rules this out as a secure means of authentication as anything that the public knows, an attacker also knows, so there is no acceptable private information in this category.
Who You Are
You specifically mention not having finger prints, but it isn't really clear about what you mean by that point. If you have public information that is validated as genuine, it may potentially be useful to authenticate someone, but verifying the authenticity of submitted information is a problem since, again, the information is available to an attacker. If you control the system taking the authentication measurements you can make this work, but if you are working over the Internet, you are likely out of luck given the public knowledge constraint.
What You Have
If people have some form of publicly validated cryptographic ID, this could be used for authentication. Similarly, if they do not, you could use a one time authentication via biometric measures and then issue a cryptographic ID that could be used for authentication. If authenticating in person, non-cryptographic IDs could also be used. That said, there is still the potential issue of theft. What You Have, on it's own, is a relatively weak form of authentication as it is the only one of the three factors that is trivially compromised via theft.
As you can see, this really doesn't leave a whole lot in the way of good options. You can go for public knowledge quizzes, but often times an attacker may actually have less trouble with this than a real person. If you ask an average person for information from their credit report for example, they are likely not going to know off the top of their head and if they look it up, so can an attacker. An attacker can also have a complete enough profile on hand to compete with a real person to impersonate knowledge of their life.