# Building Scalable and Secure Multicast Delivery Infrastructure in a Local Area Network
## 3 Pseudo-Identity Based Encryption Framework
Key revocation is one of the major problems in identity-based encryption. In the event that a private key is compromised, a user may not be offered a new key-pair. This is because the user's public-key represent his/her publicly known identity like email address, phone number etc., which are hard to change. Since the identity-based cryptography still relies on a trusted third-party for obtaining the private key and the master public-key, it still suffers from a single point failure. In [8], [PERSON] introduced the concept of Pseudo-identity based encryption. Pseudo-identity based encryption uses the publicly available identity (such as email or mobile number) as the user's public-key. This concept is borrowed from the Identity-based cryptography. However, his proposed system work without the CA. In addition, his proposal is less computationally intensive than the identity-based encryption. In this section, we modify the pseudo-identity based encryption to be used in a LAN environment. Since the pseudo-identity based encryption algorithm is based on threshold cryptographic scheme, we briefly present an overview of [PERSON]'s [9] threshold cryptographic scheme for completeness. Threshold cryptography was introduced by [PERSON] (2018). In a (\(k\), \(n\))-threshold cryptographic scheme, the secret key \(d\) is divided among \(n\)-shareholders such that  
* Any adversary can compute the global secret key \(d\) by knowing \(k\) or more shares. * It is impossible to compute the global secret key \(d\) by knowing (\(k\)-1) or fewer shares. In a \(k\)-threshold cryptographic-system, the number \(k\) is chosen in such a way that an adversary can break-in at most (\(k\)-1) shareholders. Until recently, only organizations such as militaries, governmental agencies, and certificate authorities were using this technology. However, after a October 2012 attack ([PERSON] et al., 2012) targeting large public websites using ciphertext-compromise, RSA made this technology publicly available. One of the salient features of a \(k\)-threshold cryptosystem is that any \(k\) or more shareholders can collaborate to create a new shareholder, and create a digital certificate using the global secret key. The threshold cryptography is based on polynomial-interpolation. For a detailed work on creating a share and digital signatures, please refer to [PERSON] (2018). In a threshold cryptographic scheme, the private share of each shareholder may not have any direct relation with the underlying public-key cryptography. Thus, a private share does not need to have a public-key component. In our earlier paper Shamir (2018), we combined the best features of both identity-based encryption and the threshold cryptography, removed their potential weaknesses, so that the new system can be used effectively. The new system was called the Pseudo-identity based encryption. We now outline the modification made to the threshold cryptography. For detailed work, the reader may refer to our original paper Shamir (2018). * The threshold cryptographic scheme is modified in such a way that every private share has a public-key component. * A one-to-one relationship is established between a public-key component and the identity of a shareholder. However, in our earlier paper, we did not address the key-revocation issues. Since this is a very critical problem, we incorporate this feature in this paper. We also modify the protocol to suit in a LAN environment. We outline the pseudo-identity based system here. More details are presented in [PERSON] (2018). Whenever we made any modification in this paper, we describe them in detail here. As a first step, the designer must identify the underlying public-key cryptosystem. In our case, we consider RSA as our underlying public-key cryptosystem. Once this is identified, the CA must construct the global private and the public-key pair for the underlying cryptosystem.