Before answering the question, let me caution you strongly about putting your own "security system" in place. Whatever you put in place is far less likely to be secure than the login accounts system already in place in FMP. If you can find a way to use the login function rather than overlay your own security/password step, you should use the login function.
That said, I believe that there ARE times when the login function doesn't get done what needs to be done. others on the forum disagree with this...some strenuously so.
My lesser choice:
For what you're trying to do, why not leave Field1 off of the layout entirely and run a script with "Show Custom Dialog" which pops up a little window asking for the password. The Show Custom Dialog function lets you cover up the entry so others can't read it. When setting up the field inputs for the Custom Dialog, have the user enter the value of Field1, but don't put Field1 on the layout. Now field1 data entry is hidden during entry, and is hidden by not being on the layout.
My greater choice:
Restrict user access under Accounts&Privileges so that only people who know to type in "Allow" are allowed into the filed in the first place. If an unauthorized person knows to type in "allow", they can't do it anyway because they can't get into the field. In this way you can use the built-in securit features in FMP and not invent your own.
Does this fit your applications?