Message Authentication Code over a Wiretap Channel

Message Authentication Code (MAC) is a keyed function $f_K$ such that when Alice, who shares the secret $K$ with Bob, sends $f_K(M)$ to the latter, Bob will be assured of the integrity and authenticity of $M$. Traditionally, it is assumed that the channel is noiseless. However, Maurer showed that in this case an attacker can succeed with probability $2^{-\frac{H(K)}{\ell+1}}$ after authenticating $\ell$ messages. In this paper, we consider the setting where the channel is noisy. Specifically, Alice and Bob are connected by a discrete memoryless channel (DMC) $W_1$ and a noiseless but insecure channel. In addition, an attacker Oscar is connected with Alice through DMC $W_2$ and with Bob through a noiseless channel. In this setting, we study the framework that sends $M$ over the noiseless channel and the traditional MAC $f_K(M)$ over channel $(W_1, W_2)$. We regard the noisy channel as an expensive resource and define the authentication rate $\rho_{auth}$ as the ratio of message length to the number $n$ of channel $W_1$ uses. The security of this framework depends on the channel coding scheme for $f_K(M)$. A natural coding scheme is to use the secrecy capacity achieving code of Csisz\'{a}r and K\"{o}rner. Intuitively, this is also the optimal strategy. However, we propose a coding scheme that achieves a higher $\rho_{auth}.$ Our crucial point for this is that in the secrecy capacity setting, Bob needs to recover $f_K(M)$ while in our coding scheme this is not necessary. How to detect the attack without recovering $f_K(M)$ is the main contribution of this work. We achieve this through random coding techniques.Comment: Formulation of model is change

A Critical Examination to the Unitarized ππ\pi\pi Scattering Chiral Amplitudes

We discuss the Pad\'e approximation to the $\pi\pi$ scattering amplitudes in 1--loop chiral perturbation theory. The approximation restores unitarity and can reproduce the correct resonance poles, but the approximation violates crossing symmetry and produce spurious poles on the complex $s$ plane and therefore plagues its predictions on physical quantities at quantitative level. However we find that one virtual state in the IJ=20 channel may have physical relevance.Comment: 13 pages + 4 eps figures submit to Commun. Theor. Phy

Knowledge Discovery and Complex Network Dynamics in Social Media Space

Pattern discovery and correlation in text data have been research hotbed in recent times. However, a composite model that captures patterns and correlations as a quantitative measure in social media space is yet to receive much research attention. The paper therefore analyzed social media data from Twitter about the 2014-FIFA World Cup both as lexical text and a complex network system. Quantitatively it is discovered that the 140 character upper bound in Twitter does not have negative impact on the formation of ideas. For as a lexical text, the following key statistics were confirmed: the distribution of the words in the corpus obeys a Zipf’s law, 3-character length words accounted for almost 22% of the corpus and the distribution of the article "the" also follows a Zipf’s or power-law. Moreover, the three most frequent terms related to the world cup event, that is (url, worldcup, rt) account for about 14.5% of the corpus. In particular, the corpus is modeled as a network,  where 12 V">  is the set of vocabularies in the corpus and  is the set of bigrams (two words phrases). An algorithm is developed and implemented in python to obtain the bigrams from the corpus. Using concepts from graph theory, the bigram network is analyzed and the results show compelling facts about text network. Firstly, all the characteristics of complex networks known in literature are observed in the bigram network. These include the degree distribution, which is observed to follow power-law with degree exponent  value of 2.14. Secondly, the average path length of words is observed to be 4.78, which is within the ”small world” categories. Thirdly, other complex network characteristics such as eigenvector and betweenness centralities metrics are observed within the bigram network both having weak power-law distributions as observed in other complex networks in literature. These findings call for the need to study the topological characteristics of text data and comparing their structural properties to that of known complex network metrics in literature. The results will be of great importance in studying complex systems. Also the application areas of these findings are numerous ranging from information retrieval, data compression to information security. To the best of our knowledge, this is the first work that studied the textual and topological structure of text from social media platform as a complex network and analyzed important topological properties of complex network on it. Keywords: complex network, bigram, media space, Twitter, information scienc

A Note on Secure Key Issuing in ID-based Cryptography

Most recently, Lee B. et al proposed a key issuing protocol for ID-based cryptography to solve the key escrow problem. However in this letter, we show that a malicious key generation center (KGC) can successfully attack the protocol to obtain users¡¯ private keys. This means that in the protocol, the key escrow problem isn¡¯t really removed