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Abstract
With the advent in computer and communications technologies, data is now being produced, communicated and ultimately consumed in digital form. While this brought with it a wealth of useful applications, however, due to the ease of copying and manipulating digital data, developing effective mechanisms for safeguarding digital media has become an impelling need. Various cryptographic primitives have evolved with time to meet the ever growing needs of digital communications systems in both military and civilian applications. The primary goal of the current thesis is the study, analysis and development of these cryptographic primitives. The proposed developments are required to balance several contradicting performance measures (preserving confidentiality of transactions, users privacy, the ability to trace illegal transactions, computational efficiency and speed of used algorithms). Thanks to Allah the thesis successfully presented several contributions along these directions, especially in the field of public key cryptosystems using recently developed cryptographic tools based on elliptic curves.First, as a means for preserving anonymity of customers in e-commerce applications, two new blind identity-based signature schemes have been proposed. Based on those schemes, a digital payment system has been proposed, where the anonymity of participants in some suspicious transaction can be revoked.
Second, a comprehensive survey of the state-of-the-art broadcast encryption schemes has been provided. Broadcast encryption schemes are mechanisms by which a transmission centre can securely broadcast the digital media to a dynamically changing subset of system subscribers. An interesting subclass of broadcast encryption schemes is the class of trace and revoke schemes. These schemes allow tracing the source of piracy and then revoking it from all future transmissions. A new trace and revoke scheme, based on Lagrange interpolation in the exponent, with chosen ciphertext security has been proposed. Moreover, the scalability of the scheme is explored in order to allow the support of an unlimited number of traitors. Furthermore, a guiding discussion on how to choose among the schemes surveyed based on the application in hand is also provided.
Third, new multi-recipient signcryption schemes achieving both confidentiality of the message transmitted and the authenticity of its origin are proposed. The first of them employs a carefully designed polynomial, such that only the intended set of recipients can recover the session key embedded in the constant term of the polynomial. This reduces the computational load as well as the communications overhead compared to other schemes in the literature. For security purposes, the algorithm should be implemented and distributed hard-wired in tamper- resistant devices. The second scheme is more secure and is based on polynomial interpolation in the exponent. However, the second scheme is less effici,ent. The third scheme is an identity- based signcryption scheme. The security of the scheme is formally proven in the random oracle model. Those schemes produce ciphertexts linear in the number of the recipients. Finally, a new identity-based signcryption scheme based on arranging the system users as leaf nodes in a logical binary structure is proposed. The ciphertext length and computational load are reduced to almost logarithmic order for small subsets of revoked users.
Fourth, the notion of proxy agents for generating the computationally resource demanding digital signatures has been considered. Proxy agents are usually powerful computers to which.