# Building Scalable and Secure Multicast Delivery Infrastructure in a Local Area Network
## 3 Pseudo-Identity Based Encryption Framework  
Identity-based cryptography is a system where a receiving host's publicly known identity is used as his/her public-key. This feature eliminates the need for having a PKI. However, Identity-based encryption has several implementation-related issues and key revocation problems. A \(k\)-threshold cryptography is a cryptosystem where \(k\) or more shareholders can collaboratively perform the role of a PKI (or a CA). Thus, this system is immune to single-point failure. In this section, we present a smart digital certificate mechanism using a modified threshold cryptography scheme called the Pseudo-identity based encryption. This framework combines the best features from both the identity and the \(k\)-threshold cryptographic systems. Our proposed scheme identifies the origin of every message sent in a multicast tree. Since the keys are not forgeable, any such malicious activities are immediately known to the receiving host and the servers, thus facilitating key revocation action. The main advantage of our proposed scheme is that it can work without constant access to a public-key Infrastructure or a Certificate Authority. Our schemesatisfies the identical security requirements as that of the underlying public-key cryptography and incurs the same memory and run-time complexity. As we mentioned in Section 2.1, using one key for all end-hosts and networking devices is not an efficient strategy. It does not identify a legitimate server against a malicious end-host. In addition, key revocation is an issue. Whenever a host leaves a system, a new key must be installed on to every existing device. This process is labor-intensive. Public key cryptosystem and digital certificates can be used to identify servers and end-hosts. They also provide efficient admission control. However, in order for a public-key cryptosystem to function well in a network, every host must have a secure channel to the CA. This causes maintenance overhead and is a single point failure. Since public-key cryptography answers all the three problems we posted in Section 2, it is desirable to use a public-key cryptosystem with the flexibility of not having a constant connection with the CA. Identity-based cryptography is a class of public-key cryptography proposed by [PERSON] [4]. This scheme uses a publicly known string such as an individual's name, organization, email address domain name, phone number, etc. as a public-key. [PERSON]'s scheme uses a trusted third party to deliver private keys to users upon verification of their identity. This process is similar to the issuance of a certificate in a PKI. Identity-based encryption is attractive as there is no need to fetch the public key of the receiver before encryption. Even though [PERSON] proposed this framework, he was unable to provide a concrete implementation. Thus, the identity-based encryption remains an open problem for several years. His conjecture was independently solved by [PERSON] and [PERSON] [5] and [PERSON] [6]. [PERSON] and [PERSON]'s solution is based on Weil Pairing and used the Bilinear Diffie-Hellman (BDH) framework over an elliptical curve finite field as their underlying hard problem. Their algorithm is called BasicIdent. It has been proved that in a random-oracle model, the protocol is semantically secure under the BDH assumption. Even though their algorithm is computationally secure, it is not chosen cipher-text secure. However, Fujisaki-Okamoto transformation allows for conversion to a scheme having this property called FullIdent [7]. Due to its high CPU and memory requirements, it is hard to implement this algorithm in every environment. Compared to [PERSON] and [PERSON]'s model, [PERSON]'s solution is easy to implement. His solution used the traditional quadratic residues modulo problem as their underlying hard-problem. However, as his solution uses bit-by-bit encryption, it is not economical. In addition, [PERSON]'s solution does not preserve the identity of a recipient. This is done by passively observing the ciphertext.