Biblio

All-or-nothing transforms (AONT) were proposed by Rivest as a message preprocessing technique for encrypting data to protect against brute-force attacks, and have many applications in cryptography and information security. Later the unconditionally secure AONT and their combinatorial characterization were introduced by Stinson. Informally, a combinatorial AONT is an array with the unbiased requirements and its security properties in general depend on the prior probability distribution on the inputs s-tuples. Recently, it was shown by Esfahani and Stinson that a combinatorial AONT has perfect security provided that all the inputs s-tuples are equiprobable, and has weak security provided that all the inputs s-tuples are with non-zero probability. This paper aims to explore on the gap between perfect security and weak security for combinatorial (t, s, v)-AONTs. Concretely, we consider the typical scenario that all the s inputs take values independently (but not necessarily identically) and quantify the amount of information H(\textbackslashmathcalX\textbackslashmid \textbackslashmathcalY) about any t inputs \textbackslashmathcalX that is not revealed by any s−t outputs \textbackslashmathcalY. In particular, we establish the general lower and upper bounds on H(\textbackslashmathcalX\textbackslashmid \textbackslashmathcalY) for combinatorial AONTs using information-theoretic techniques, and also show that the derived bounds can be attained in certain cases.

Data can be stored securely in various storage servers. But in the case of a server failure, or data theft from a certain number of servers, the remaining data becomes inadequate for use. Data is stored securely using secret sharing schemes, so that data can be reconstructed even if some of the servers fail. But not much work has been carried out in the direction of updation of this data. This leads to the problem of updation when two or more concurrent requests arrive and thus, it results in inconsistency. Our work proposes a novel method to store data securely with concurrent update requests using Petri Nets, under the assumption that the number of nodes is very large and the requests for updates are very frequent.

We consider transmissions of secure messages over a burst erasure wiretap channel under decoding delay constraint. For block codes we introduce and study delay optimal secure burst erasure correcting (DO-SBE) codes that provide perfect security and recover a burst of erasures of a limited length with minimum possible delay. Our explicit constructions of DO-SBE block codes achieve maximum secrecy rate. We also consider a model of a burst erasure wiretap channel for the streaming setup, where in any sliding window of a given size, in a stream of encoded source packets, the eavesdropper is able to observe packets in an interval of a given size. For that model we obtain an information theoretic upper bound on the secrecy rate for delay optimal streaming codes. We show that our block codes can be used for construction of delay optimal burst erasure correcting streaming codes which provide perfect security and meet the upper bound for a certain class of code parameters.

Consider a synchronous distributed network which is partly controlled by an adversary. In a Perfectly Secret Message Transmission(PSMT) protocol, the sender S wishes to transmit a message to the receiver R such that the adversary learns nothing about the message. We characterize the set of directed graphs that admit PSMT protocols tolerating a dual failure model where up to tp nodes are passively corrupted and further up to any tf nodes may fail.