Paper 2016/739

Unconditionally Secure Signatures

Ryan Amiri, Aysajan Abidin, Petros Wallden, and Erika Andersson

Abstract

Digital signatures are one of the most important cryptographic primitives. In this work we construct an information-theoretically secure signature scheme which, unlike prior schemes, enjoys a number of advantageous properties such as short signature length and high generation efficiency, to name two. In particular, we extend symmetric-key message authentication codes (MACs) based on universal hashing to make them transferable, a property absent from traditional MAC schemes. Our main results are summarised as follows. - We construct an unconditionally secure signature scheme which, unlike prior schemes, does not rely on a trusted third party or anonymous channels. In our scheme, a sender shares with each of the remaining protocol participants (or recipients) a set of keys (or hash functions) from a family of universal hash functions. Also, the recipients share with each other a random portion of the keys that they share with the sender. A signature for a message is a vector of tags generated by applying the hash functions to the message. As such, our scheme can be viewed as an extension of MAC schemes, and therefore, the practical implementation of our scheme is straightforward. - We prove information-theoretic security of our scheme against forging, repudiation, and non-transferability. - We compare our schemes with existing both "classical" (not employing quantum mechanics) and quantum unconditionally secure signature schemes. The comparison shows that our new scheme has a number of unparalleled advantages over the previous schemes. - Finally, although our scheme does not rely on trusted third parties, we discuss this, showing that having a trusted third party makes our scheme even more attractive.