Whereas quantum cryptography ensures security by virtue of complete indistinguishability of nonorthogonal quantum states attenuation in quantum communication channels and unavailability of single-photon sources present major problems. In view of these difficulties the security of quantum cryptography can change from unconditional to conditional. Since the restrictions imposed by nonrelativistic quantum mechanics and used to formulate key distribution protocols are largely exhausted new principles are required. The fundamental relativistic causality principle in quantum cryptography can be used to propose a new approach to ensuring unconditional security of quantum cryptosystems that eliminates the aforementioned difficulties. Quantum cryptosystems of this kind should obviously be called relativistic. It is shown that relativistic quantum cryptosystems remain unconditionally secure: first attenuation in a quantum communication channel can only reduce the key generation rate but not the security of the key second the source may not generate pure single-photon states and a nonzero single-photon probability will suffice. The scheme remains secure even if the contribution of a single-photon component is arbitrarily small. This formally implies that a state may be characterized by an arbitrarily large mean photon number. The single-photon probability affects only the key generation rate but not security.