International Association
for Cryptologic Research

In a digital signature scheme with message recovery, rather than transmitting the message $m$ and its signature $\\sigma$, a single enhanced signature $\\tau$ is transmitted. The verifier is able to recover $m$ from $\\tau$ and at the same time

verify its authenticity. The two most important parameters of such a scheme are its security and the overhead $|\\tau|-|m|$. A simple argument shows that for any scheme with ``$n$ bits security\" $|\\tau|-|m|\\ge n$, i.e., the overhead is at least the security. The best previous constructions required an overhead of $2n$. In this paper we show that the $n$ bit lower bound can basically be matched. Concretely, we propose a new simple RSA-based digital signature scheme that, for $n=80$ bits security in the random oracle model, has an overhead of $\\approx 90$ bits.

At the core of our security analysis is an almost tight upper bound for the expected number of edges of the densest ``small\'\' subgraph of a random Cayley graph, which may be of independent interest.