Data security is one of the prime concerns in wireless networks. PLKG has been emerging as an attractive alternative to traditional cryptographic techniques. PLKG is more computationally efficient than cryptography. Moreover, PLKG using Principal component analysis (PCA) as pre-processing may further save computations. This paper proposes three mechanisms to select components of PCA which are based on Information content, Mean and Histfit. Bit Disagreement Rate (BDR) is compared for each mechanism. Histfit based method is found to be best. Since only two components are supposed to be processed for key generation, it is computationally efficient/ power efficient too.
We show an Ω(√n/T) lower bound for the space required by any unidirectional constant-error randomized T-pass streaming algorithm that recognizes whether an expression over two types of parenthesis is well parenthesized. This proves a conjecture due to Magniez, Mathieu, and Nayak (2009) and rigorously establishes that bidirectional streams are exponentially more efficient in space usage as compared with unidirectional ones. We obtain the lower bound by analyzing the information that is necessarily revealed by the players about their respective inputs in a two-party communication protocol for a variant of the index function, namely augmented index. We show that in any communication protocol that computes this function correctly with constant error on the uniform distribution (a “hard” distribution), either Alice reveals Ω(n) information about her n-bit input, or Bob reveals Ω(1) information about his (logn)-bit input, even when the inputs are drawn from an “easy” distribution, the uniform distribution over inputs that evaluate to 0. The information cost tradeoff is obtained by a novel application of the conceptually simple and familiar ideas, such as average encoding and the cut-and-paste property, of randomized protocols. Motivated by recent examples of exponential savings in space by streaming quantum algorithms, we also study quantum protocols for augmented index. Defining an appropriate notion of information cost for quantum protocols involves a delicate balancing act between its applicability and the ease with which we can analyze it. We define a notion of quantum information cost, which reflects some of the nonintuitive properties of quantum information. We show that in quantum protocols that compute the augmented index function correctly with constant error on the uniform distribution, either Alice reveals Ω(n/t) information about her n-bit input, or Bob reveals Ω(1/t) information about his (log n)-bit input, where t is the number of messages in the protocol, even when the inputs are drawn from the abovementioned easy distribution. While this tradeoff demonstrates the strength of our proof techniques, it does not lead to a space lower bound for checking parentheses. We leave such an implication for quantum streaming algorithms as an intriguing open question.
An explicit algorithm for performing Schumacher's noiseless compression of quantum bits is given. This algorithm is based on a combinatorial expression for a particular bijection among binary strings. The algorithm, which adheres to the rules of reversible programming, is expressed in a high-level pseudocode language. It is implemented using O(n3) two- and three-bit primitive reversible operations, where n is the length of the qubit strings to be compressed. Also, the algorithm makes use of O(n) auxiliary qubits. Space-saving techniques based on those proposed by Bennett are developed which reduce this workspace to O(\ensuremath{\surd}n) while maintaining a running time of O(n3) (albeit with a larger constant). This latter algorithm is of interest because it has a slightly smaller time-space product, which is considered to be the relevant figure of merit for efficiency in some physical models. \textcopyright{} 1996 The American Physical Society.