In Information Processing Letters (2006), Tan pointed out that the anonymous signcryption scheme proposed by Yang, Wong and Deng (YWD) in ISC 2005 provides neither confidentiality nor anonymity. However, no discussion has been made on how a secure scheme can be made and there is no secure scheme available to date. In this paper, we propose a modification of YWD scheme which resolves the security issues of the original scheme without sacrificing its high efficiency and simple design. Indeed, we show that our scheme achieves confidentiality, existential unforgeability and anonymity with more precise reduction bounds. We also give a variation of our scheme and extend it to a ring signcryption scheme by using the technique due to Boneh, Gentry, Lynn and Shacham. © 2010 IOS Press and the authors.