Cryptanalysis and Improvement of Shacham-Waters Ring Signature Scheme

Shacham-waters proposed an efficient ring signature scheme without random oracle, and proved that it¿s unforgeable in their security model. But, it¿s insecure in another security model proposed by Masayuki Abe et al. This article shows an existential forgery attack on the scheme, and improves this scheme in order to resist this attack.