The same way that FAT has file attributes (archive, system file, invisible), GNU/Linux filesystems has its own, but they are different. We'll briefly go over them here for the sake of completeness, but they are very seldom used. However, if you really want a secure system, read on.
There are two commands for manipulating file attributes: lsattr(1) and chattr(1). You probably guessed it, lsattr LiSts attributes, whereas chattr CHanges them. These attributes can only be set on directories and regular files. The following attributes are possible:
A (no Access time): if a file or directory has this attribute set, whenever it is accessed, either for reading of for writing, its last access time will not be updated. This can be useful, for example, on files or directories which are often accessed for reading, especially since this parameter is the only one which changes on an inode when it's open read-only.
a ( append only): if a file has this attribute set and is open for writing, the only operation possible will be to append data to its previous contents. For a directory, this means that you can only add files to it, but not rename or delete any existing file. Only root can set or clear this attribute.
d (no dump): dump (8) is the standard UNIX utility for backups. It dumps any filesystem for which the dump counter is 1 in /etc/fstab (see chapter Chapter 8, File Systems and Mount Points). But if a file or directory has this attribute set, unlike others, it will not be taken into account when a dump is in progress. Note that for directories, this also includes all subdirectories and files under it.
i ( immutable): a file or directory with this attribute set can not be modified at all: it can not be renamed, no further link can be created to it [23] and it cannot be removed. Only root can set or clear this attribute. Note that this also prevents changes to access time, therefore you do not need to set the A attribute when i is set.
s ( secure deletion): when a file or directory with this attribute is deleted, the blocks it was occupying on disk are overwritten with zeroes.
S ( Synchronous mode): when a file or directory has this attribute set, all modifications on it are synchronous and written to the disk immediately.
For example, you may want to set the i attribute on essential system files in order to avoid bad surprises. Also, consider the A attribute on man pages: this prevents a lot of disk operations and, in particular, can save some battery life on laptops.