The Exact Price for Unconditionally Secure Asymmetric Cryptography

A completely insecure communication channel can only be transformed into an unconditionally secure channel if some information-theoretic primitive is given to start from. All previous approaches to realizing such authenticity and privacy from weak primitives were symmetric in the sense that security for both parties was achieved. We show that asymmetric information-theoretic security can, however, be obtained at a substantially lower price than two-way security-like in the computational-security setting, as the example of public-key cryptography demonstrates. In addition to this, we show that also an unconditionally secure bidirectional channel can be obtained under weaker conditions than previously known. One consequence of these results is that the assumption usually made in the context of quantum key distribution that the two parties share a short key initially is unnecessarily strong.