We start by abstracting the recent work of Hohenberger and Waters (Crypto 2009), and specifically their ``prefix method''. We show a transformation taking a signature scheme with a very weak security guarantee (a notion that we call a-priori-message unforgeability under static chosen message attack) and producing a fully secure signature scheme (i.e., existentially unforgeable under adaptive chosen message attack). Our transformation uses the notion of chameleon hash functions, defined by Krawczyk and Rabin (NDSS 2000) and the ``prefix method''. Constructing such weakly secure schemes seems to be significantly easier than constructing fully secure ones, and we present {\em simple} constructions based on the RSA assumption, the {\em short integer solution} (SIS) assumption, and the {\em computational Diffie-Hellman} (CDH) assumption over bilinear groups.
Next, we observe that this general transformation also applies to the regime of ring signatures. Using this observation, we construct new (provably secure) ring signature schemes: one is based on the {\em short integer solution} (SIS) assumption, and the other is based on the CDH assumption over bilinear groups. As a building block for these constructions, we define a primitive that we call \emph{ring trapdoor functions}. We show that ring trapdoor functions imply ring signatures under a weak definition, which enables us to apply our transformation to achieve full security.
Finally, we show a connection between ring signature schemes and identity based encryption (IBE) schemes. Using this connection, and using our new constructions of ring signature schemes, we obtain two IBE schemes: The first is based on the {\em learning with error} (LWE) assumption, and is similar to the recently introduced IBE scheme of Cash-Hofheinz-Kiltz-Peikert; The second is based on the $d$-linear assumption over bilinear groups.
Category / Keywords: public-key cryptography / digital signatures, ring signatures, identity based encryption Date: received 17 Feb 2010, last revised 16 Nov 2010 Contact author: zvika brakerski at weizmann ac il Available formats: PDF | BibTeX Citation Version: 20101116:195359 (All versions of this report) Discussion forum: Show discussion | Start new discussion