We address the security issue of RSA with implicitly related keys in this paper. Informally, we investigate under what condition is it possible to efficiently factorize RSA moduli in polynomial time given implicit relation of the related private keys that certain portions of bit pattern are the same. We formulate concrete attack scenarios and propose lattice-based cryptanalysis by using lattice reduction algorithms. A subtle lattice technique is adapted to represent an unknown private key with the help of known implicit relation. We analyze a simple case when given two RSA instances with the known amount of shared most significant bits (MSBs) and least significant bits (LSBs) of the private keys. We further extend to a generic lattice-based attack for given more RSA instances with implicitly related keys. Our theoretical results indicate that RSA with implicitly related keys is more insecure and better asymptotic results can be achieved as the number of RSA instances increases. Furthermore, we conduct numerical experiments to verify the validity of the proposed attacks.

This paper presents a novel statistic computation technique for energy detection-based spectrum sensing with multiple antennas. The presented technique computes the statistic for signal detection after combining all the signals. Because the computation of the statistic for all the received signals is not required, the presented technique reduces the computational complexity. Furthermore, the absolute value of all the received signals are combined to prevent the attenuation of the combined signals. Because the statistic computations are not required for all the received signals, the reduction of the computational complexity for signal detection can be expected. Furthermore, the presented technique does not need to choose anything, such as the binary phase rotator in the conventional technique, and therefore, the performance degradation due to wrong choices can be avoided. Numerical examples indicate that the spectrum sensing performances of the presented technique are almost the same as those of conventional techniques despite the complexity of the presented technique being less than that of the conventional techniques.

This paper presents a novel spectrum sensing technique based on selection diversity combining in cognitive radio networks. In general, a selection diversity combining scheme requires a period to select an optimal element, and spectrum sensing requires a period to detect a target signal. We consider that both these periods are required for the spectrum sensing based on selection diversity combining. However, conventional techniques do not consider both the periods. Furthermore, spending a large amount of time in selection and signal detection increases their accuracy. Because the required period for spectrum sensing based on selection diversity combining is the summation of both the periods, their lengths should be considered while developing selection diversity combining based spectrum sensing for a constant period. In reference to this, we discuss the spectrum sensing technique based on selection diversity combining. Numerical examples are shown to validate the effectiveness of the presented design techniques.

Boolean networks (BNs) are considered as popular formal models for the dynamics of gene regulatory networks. There are many different types of BNs, depending on their updating scheme (synchronous, asynchronous, deterministic, or non-deterministic), such as Classical Random Boolean Networks (CRBNs), Asynchronous Random Boolean Networks (ARBNs), Generalized Asynchronous Random Boolean Networks (GARBNs), Deterministic Asynchronous Random Boolean Networks (DARBNs), and Deterministic Generalized Asynchronous Random Boolean Networks (DGARBNs). An important long-term behavior of BNs, so-called attractor, can provide valuable insights into systems biology (e.g., the origins of cancer). In the previous paper [1], we have studied properties of attractors of GARBNs, their relations with attractors of CRBNs, also proposed different algorithms for attractor detection. In this paper, we propose a new algorithm based on SAT-based bounded model checking to overcome inherent problems in these algorithms. Experimental results prove the effectiveness of the new algorithm. We also show that studying attractors of GARBNs can pave potential ways to study attractors of ARBNs.

In this letter, the principle of LLR-based successive-cancellation (SC) polar decoding algorithm is explored. In order to simplify the logarithm and exponential operations in the updating rules for polar codes, we further utilize a piece-wise linear algorithm to approximate the transcendental functions, where the piece-wise linear algorithm only consists of multiplication and addition operations. It is demonstrated that with one properly allowable maximum error δ chosen for success-failure algorithm, performances approach to that of the standard SC algorithm can be achieved. Besides, the complexity reduction is realized by calculating a linear function instead of nonlinear function. Simulation results show that our proposed piece-wise SC decoder greatly reduces the complexity of the SC-based decoders with no loss in error correcting performance.