Number-Theoretic Attack on Lyuu-Wu's Multi-proxy Multi-signature Scheme

Y. D. Lyuu and M. L. Wu had proposed an improved multi-proxy multi-signature scheme, which was claimed to resist the forge attack. Lately, L. Guo and G. Wang found an inside attack on the Lyuu-Wu's scheme. In this paper, we propose a new attack on Lyuu-Wu's scheme, which can factor the parameter $N$ and $Q$ by using efficient number-theoretic algorithms when $Q$ is roughly larger than the square root of $N$. It follows that Lyuu-Wu's scheme suffers from the forge attack from the proxy signers in that case.