Fully distributed threshold rsa under standard assumptions

Abstract. The aim of this article is to propose a fully distributed envi-ronment for the RSA scheme. What we have in mind is highly sensitive applications and even if we are ready to pay a price in terms of e±-ciency, we do not want any compromise of the security assumptions that we make. Recently Shoup proposed a practical RSA threshold signature scheme that allows to share the ability to sign between a set of players. This scheme can be used for decryption as well. However, Shoup's pro-tocol assumes a trusted dealer to generate and distribute the keys. This comes from the fact that the scheme needs a special assumption on the RSA modulus and this kind of RSA moduli cannot be easily generated in an e±cient way with many players. Of course, it is still possible to call theoretical results on multiparty computation, but we cannot hope to design e±cient protocols. The only practical result to generate RSA moduli in a distributive manner is Boneh and Franklin's protocol but it seems di±cult to modify it in order to generate the kind of RSA moduli that Shoup's protocol requires. The present work takes a di®erent path by proposing a method to en-hance the key generation with some additional properties and revisits Shoup's protocol to work with the resulting RSA moduli. Both of these enhancements decrease the performance of the basic protocols. However, we think that in the applications we target, these enhancements provide practical solutions. Indeed, the key generation protocol is usually run only once and the number of players used to sign or decrypt is not very large. Moreover, these players have time to perform their task so that the communication or time complexity are not overly important