Ethics is a complicated subject, but if you are looking for "core", that is universally accepted principles, you are going to bump against metaphysical issues, like selecting an acceptable ontology to encompass all being. What constitutes morality will differ widely among philosophers depending on their school of thought. In fact, some philosophers may argue no "core principles" exist at all.

I have heard many learned men and women speak of the Golden Rule as the universal human characteristic endemic to morality, and perhaps a scientific examination of the evolution of the human mind might substantiate this. Frans de Waal, the noted primatologist has raised a number of questions and asserted widely that morality has its roots in our mammalian, particularly our hominid ancestry.

In the volume Primates and Philosophers, de Waal, Peter Singer, Christine Koorsgard, and others debate the evolution of morality. As such, before you come to your own conclusions if there are "core principles" and determine what those core principles are, it would behoove you to study the evolutionary perspective of the origins of moral behavior (presuming you accept science and evolution as fact, which certainly not everyone does).

According to the perspectives of the aforementioned work, it has been argued that the behavioral component common to us and our closest relatives is not just reciprocal altruism, but psychological altruism, which is defined much more narrowly than the more general notion of biological altruism, concepts advocated by sociobiologists.

One possible philosophical extension of the Golden Rule is Kant's interpretation of morality from The Critique of Pure Reason, whereby one takes one's desire and formulates a maxim, which is the recognition that the exercise of agency for an end must be tested against the Categorical Imperative. Doing so elevates a desire from mere desire, to justified choice, a process that represents the deepest intentionality possible in agency, making one a moral agent.

Ultimately, if a foundation for morality is found to encompass one or more "core principles", it is likely to be promoted by an empirical camp of thinking, such as evolutionary psychology which seeks to track down universals in human decision making within the context of human evolution.