Byzantine Modification Detection in Multicast Networks With Random Network Coding

An information-theoretic approach for detecting Byzantine or adversarial modifications in networks employing random linear network coding is described. Each exogenous source packet is augmented with a flexible number of hash symbols that are obtained as a polynomial function of the data symbols. This approach depends only on the adversary not knowing the random coding coefficients of all other packets received by the sink nodes when designing its adversarial packets. We show how the detection probability varies with the overhead (ratio of hash to data symbols), coding field size, and the amount of information unknown to the adversary about the random code

Secure message transmission in the general adversary model

The problem of secure message transmission (SMT), due to its importance in both practice and theory, has been studied extensively. Given a communication network in which a sender S and a receiver R are indirectly connected by unreliable and distrusted channels, the aim of SMT is to enable messages to be transmitted from S to R with a reasonably high level of privacy and reliability. SMT must be achieved in the presence of a Byzantine adversary who has unlimited computational power and can corrupt the transmission. In the general adversary model, the adversary is characterized by an adversary structure. We study two diff�erent measures of security: perfect (PSMT) and almost perfect (APSMT). Moreover, reliable (but not private) message transmission (RMT) are considered as a specifi�c part of SMT. In this thesis, we study RMT, APSMT and PSMT in two di�fferent network settings: point-to-point and multicast. To prepare the study of SMT in these two network settings, we present some ideas and observations on secret sharing schemes (SSSs), generalized linear codes and critical paths. First, we prove that the error-correcting capability of an almost perfect SSS is the same as a perfect SSS. Next, we regard general access structures as linear codes, and introduce some new properties that allow us to construct pseudo-basis for efficient PSMT protocol design. In addition, we de�fine adversary structures over "critical paths", and observe their properties. Having these new developments, the contributions on SMT in the aforementioned two network settings can be presented as follows. The results on SMT in point-to-point networks are obtained in three aspects. First, we show a Guessing Attack on some existing PSMT protocols. This attack is critically important to the design of PSMT protocols in asymmetric networks. Second, we determine necessary and sufficient conditions for di�fferent levels of RMT and APSMT. In particular, by applying the result on almost perfect SSS, we show that relaxing the requirement of privacy does not weaken the minimal network connectivity. Our �final contribution in the point-to-point model is to give the �first ever efficient, constant round PSMT protocols in the general adversary model. These protocols are designed using linear codes and critical paths, and they signifi�cantly improve some previous results in terms of communication complexity and round complexity. Regarding SMT in multicast networks, we solve a problem that has been open for over a decade. That is, we show the necessary and sufficient conditions for all levels of SMT in di�fferent adversary models. First, we give an Extended Characterization of the network graphs based on our observation on the eavesdropping and separating activities of the adversary. Next, we determine the necessary and sufficient conditions for SMT in the general adversary model with the new Extended Characterization. Finally, we apply the results to the threshold adversary model to completely solve the problem of SMT in general multicast network graphs