Transformation of digital signature schemes into designated confirmer signature schemes

Since designated confirmer signature schemes were introduced by Chaum and formalized by Okamoto, a number of attempts have been made to design designated confirmer signature schemes which are efficient and at the same time provably secure under standard cryptographic assumptions. Yet, there has been a consistent gap in security claims and analysis between all generic theoretical proposals and any concrete implementation proposal one can envision using in practice. In this paper we propose a modification of Okamoto's definition of security which still captures security against chosen message attack, and yet enables the design of concrete and reasonably efficient designated confirmer signature schemes which can be proved secure without resorting to random oracle assumptions as previously done. In particular, we present simple transformations of the digital signature schemes of Cramer-Shoup, Goldwasser-Micali-Rivest and Gennaro-Halevi-Rabin into secure designated confirmer signature schemes. We prove security of the schemes obtained under the same security assumption made by the digital signature scheme transformed and an encryption scheme we use as a tool.