Ring signature, formally introduced by Rivest,Shamir and Tauman in 2001 is a type of signature schemes similar to group signature schemes but have two distinct properties: spontaneity and anonymity. Spontaneity ensures that no participation or collaboration of other ring members is needed for the actual signer to form a ring (or group) of members and generate a signature on behalf of this ring. The spontaneity of these schemes is desirable for ad-hoc groups such as mobile ad-hoc networks. Anonymity means signer-ambiguous in the sense that a signature can be verified as coming from a certain ring, without revealing the identity of the actual signer. Anonymity is becoming a major concern in many multi-user electronic commerce applications such as e-cash and online games. Due to ring signature’s distinct and interesting properties, it has been studied extensively, and there are many applications for ring signature proposed. In many applications such as e-voting, e-auction and authentication protocols, we need to protect a signer’s identity from being known by eavesdroppers or other parties in a system. In threshold ring signature schemes, any group of t entities spontaneously conscript arbitrarily n?t entities to generate a publicly verifiable t-out-of-n signature on behalf of the whole group, yet the actual signers remain anonymous. In recent years, many proposals of identity based ring signature schemes have been published. In identity based cryptography systems, such as digital signature, key exchanging and secure authentication, users are not capable of generating a private key for ownselves. For this reason, there is a trusted party called the private key generator (PKG) who does the system setup. To obtain a private key for his identity, a user would go to the PKG and prove his identity. The PKG would then generate the appropriate private key and pass it on to the user. Since the PKG is able to compute the private key corresponding to any identity, it has to be completely trusted. The PKG is free to engage in malicious activities without any risk of being confronted in a court of law. The malicious activities could include: signing on behalf of user, or worse still: generating and distributing private keys for any identity. The key feature of ring signature is to protect anonymity of the signer. According to the key feature of ring signature, it is necessary to propose solutions to completely avoid signature forgery by PKG. The main goal of this thesis is to propose the solutions to avoid users’ signature forgery by PKG. In the thesis, at first, the concept of identity-based threshold ring signature and forging signature by PKG are completely described. Then, two solutions have been proposed to avoid signature forgery by PKG. In the first solution, forging signature by PKG is too difficult and in the second solution, forging signature by PKG is not possible. Finally, we propose a new identity based threshold ring signature whose security is based on the hardness of the RSA problem. This is the first identity-based threshold ring signature scheme which does not employ bilinear pairings. Furthermore, the resulting scheme satisfies an interesting property: the real oeners of a ring signature can disclose their identity every time and prove that they are persons who actually signed the message. Keywords: Ring signature, Identity-based cryptography, Private Key Generator(PKG), Secret sharing, Bilinear pairings, Thereshold ring signature