Ancient Greeks had a lot to say about the ethics of trust. While Aristotle borrowed heavily from Plato in this respect, most of what you commonly attribute to ethics and morality all start with Aristotle. Aristotle's ethics talk particularly about the ethics of trust with regard to relationships. He essentially says distrust is born when people act solely out of self-interest. They either find someone "useful, good," or "pleasant" in some shape or form that is singularly beneficial to themselves, as well. Sharing such potentially negative sensibilities is a major reason why people might try to become friends, but never wholly trust each other. They develop on a morally "defective" foundation. People may build positive trust (Aristotle ascribes this as "virtue") when they behave in ways that are beneficial to another. Modern-day moral philosophy often talks about this premise in terms of "other-regarding ethics."
Renaissance era philosopher, Niccolo Machiavelli, wrote about his own brand of ethics and trust. In this, he is generally considered the "first political moral philosopher." In "The Prince," he regards common sensibilities about morality and ethics of trust as wholeheartedly flawed. He says that people who are virtuous or trusting are often "done in," by those who do not behave as they should; universal moral notions of "right and wrong" are simply fantasy. The only way you can trust someone is by virtue of the power you hold in the relationship.
For Immanuel Kant, trust plays an integral part in the role of ethics. Because people are all essentially capable of reasoning, they should not only treat themselves with "human worth and dignity," but they should also treat every other human being the same. According to Kant, this makes all of us part of a "moral community." When you behave contrary to Kantian dignity, lying or cheating, for example, you also take away another's ability to consent to that act. False belief may breed mistrust, thereby reducing another's right to moral membership, as well.
Sigmund Freud talked about ethics of trust in terms of a theoretical division between a "private and public self." Rather than assume the existence of one, all encompassing moral ideology (such as Aristotle and Kant, for example), Freud addresses how your "patterns of life" may be modeled by a "set of rules and codes" that may direct "right and wrong behavior." Freud essentially says that people develop a moral map as they gain life experience and mature. Ethical modes of trust and behavior thereby stem from features of psychology rather than ideas of moral universality.