With the development of network technology, privacy protection and users anonymity become a new research hotspot. The existing blockchain privacy‐aware public key infrastructure (PKI) model can ensure the privacy of users in the authentication process to a certain extent, but there are still problems of the storage and leakage of users' keys. This paper first proposes a strong forward‐secure ring signature scheme based on RSA, which ensures the anonymity of the signing users and the forward‐backward security of the keys. Then, by introducing the ring signature technology into the privacy‐aware PKI model, this paper proposes a privacy‐aware PKI model with strong forward security based on block chains, which not only ensures the users' identity privacy, but also solves the problem of the storage and leakage of the users' keys, greatly improving the success rate and security of the users' identity authentication. Finally, this paper applies the proposed PKI model to anonymous transactions, designs a privacy‐aware anonymous transaction model with strong forward security, realizing anonymous transactions without relying on trusted third parties, and implementing users' privacy protection.