What follows is my interpretation of Hobbes' justification as it appears in the Leviathan . Thus, everyone has a right to self-preservation. Since it is natural for each person to avoid those things that destroy one's own life, we are justified in doing whatever we must to preserve our lives. But if everyone has a right to everything, then no one and nothing is secure.
Peace is a necessary condition for satisfying most of one's desires.
It is also a law of nature that one should relinquish the right to all things when others are willing to do the same for the sake of peace. One's rights can be relinquished either by renouncing them or by transferring them to another. If one transfers a right to another, that person gives up the freedom to exercise the right and assumes an obligation or duty not to hinder the exercise of the right by the one to whom it has been transferred, since to do so would be contradictory and unjust. Since anything done voluntarily is done in order to achieve some good, one gives up a right only if there is some good to be gained by doing so. Agreements made must be kept, otherwise they are not agreements at all.