I would like to design class A implements interface C and reduce the visibility of a method (declared in C)to make it secure from outer world, make one of the methods in in
No, you can't reduce the visibility of a method in an interface. What would you expect to happen if someone wrote:
C foo = new A();
foo.methodDeclaredPrivateInA();
? As far as the compiler is concerned, everything with a reference to an implementation of C
has the right to call any methods within it - that's what Liskov's Substitution Principle is all about.
If you don't want to implement the whole of a public interface, don't implement it - or throw exceptions if you absolutely must.
It's also worth noting that the accessibility provided in source code is rarely a good security measure. If your class is running in a VM which in turn gets to determine its own permissions, anyone can make members visible via reflection.