Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Applied Statistics Unit (ASU-Kolkata)


Sarkar, Palash (ASU-Kolkata; ISI)

Abstract (Summary of the Work)

In symmetric key cryptography, it is assumed that there are two parties Alice and Bob and there is an insecure communication channel between them as shown in Figure 1.1. A cryptographic system can be used to achieve secure communication between these two parties. This cryptographic system assumes that there is a secret K called the key that is known only to Alice and Bob and no one else. The message to be communicated is called the plaintext and is denoted by M. The cryptographic system has an encryption algorithm Enc(M, K) used by the sender that takes as input a plaintext message M and the secret key K and gives as output a ciphertext C. The receiver uses the decryption algorithm Dec(C, K) that takes as input the ciphertext C and the secret key K to recover the plaintext message M. Since the secret key K is not known to anybody other than Alice and Bob, no one else can succeed in decrypting the ciphertext C with non-negligible probability.Now consider a scenario where there are n+ 1 parties such that one of them is the sender and the remaining n are receivers as shown in Figure 1.2. The sender here is called the center who broadcasts encrypted messages to the n receivers called the users of the system. Let N be the set of users. In a particular session, some of the users are privileged and hence they can correctly decrypt the message. The decryption privilege of the remaining users are revoked. Let R be the set of revoked users. Assuming there are r = |R| revoked users, theremaining n−r users are privileged. The cryptographic framework that ensures the working of the above system is called Broadcast Encryption (BE). A Broadcast Encryption (BE) scheme allows the center to efficiently broadcast encrypted information so that only the privileged users in N \\ R can decrypt the message correctly. The privileged set can be any subset of N . In the two-party system, we have seen that a single secret key is shared between Alice and Bob while the algorithms Enc and Dec and all other parameters in the system are public. The use of this secret key ensures that no third party will be able to correctly decrypt the ciphertext. We first look at two basic techniques for designing a BE scheme using such a two-party symmetric key encryption scheme. Singleton Set Scheme. In the first technique, a unique secret key is assigned to every user in N . Each of these secret keys are known to the broadcasting center. The two-party symmetric key scheme can hence be used to communicate between the center and each user. Hence, the center encrypts the plaintext message M using the secret key of each privileged user in N \\ R. All thesen − r encryptions of M are broadcast through the common public channel. Only a user in N \\ R should be able to decrypt the plaintext message M from the portion of this broadcast intended for itself.


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Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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Mathematics Commons