Lattice-reduction-aided MMSE precoding for correlated MIMO channels and performance analysis

The lattice-reduction （LR） has been developed to im- prove the performance of the zero-forcing （ZF） precoder in multiple input multiple output （MIMO） systems. Under the assumptions of uncorrelated flat fading channel model and perfect channel state information at the transmitter （CSIT）, an LR-aided ZF precoder is able to collect the full transmit diversity. With the complex Lenstra- Lenstra-Lov^sz （LLL） algorithm and limited feedforward structure, an LR-aided linear minimum-mean-square-error （LMMSE） pre- coder for spatial correlated MIMO channels and imperfect CSIT is proposed to achieve lower bit error rate （BER）. Assuming a time division duplexing （TDD） MIMO system, correlated block flat fad- ing channel and LMMSE uplink channel estimator, it is proved that the proposed LR-aided LMMSE precoder can also obtain the full transmit diversity through an analytical approach. Furthermore, the simulation results show that with the quadrature phase shift keying （QPSK） modulation at the transmitter, the uncoded and coded BERs of the LR-aided LMMSE precoder are lower than that of the traditional LMMSE precoder respectively when Eb-No is greater than 10 dB and 12 dB at all correlation coefficients.

A Fixed-Point Iterative Method for Discrete Tomography Reconstruction Based on Intelligent Optimization

Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.

Enhanced NTRU cryptosystem eliminating decryption failures

An enhaned NTRU cryptosystem eliminating decryption failures is proposed without using padding schemes and can resist the oracle model andchosen-ciphertext attacks. Because lattice reduction is the main threat to lattice-based cryptosystems, lattice reductionalgorithms are analyzed to evaluate the security of this scheme. Furthermore, the new scheme remains the advantage of high efficiency of original NTRU.

On the Successive Minima of Subbases of Low-Dimensional Lattices

In this paper we discuss the global optimality of vector lengths for lattice bases. By introducing a partial order on lattice bases and the concept of successive minimal basis （SMB for short）, we show that any of its minimal elements is a general greedy-reduced basis, and its least element （if exists） is an SMB. Furthermore, we prove the existence of SMB for lattices of dimension up to 6.

Cryptanalysis of RSA for a special case with d>e

In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N^0.258 ≤ e ≤N^0.854, d 〉 e and satisfies the given conditions, we can perform cryptanalytic attacks based on the LLL lattice basis reduction algorithm. The idea is an extension of Boneh and Durfee＇s researches on low private key RSA, and provides a new solution to finding weak keys in RSA cryptosystems.

Probability method for cryptanalysis of general multivariate modular linear equation

Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. However, one problem arises here that if the equation has a short solution in given bounded range, the results outputted by earlier algorithms are often not the ones we are interested in. In this paper, we present a probability method based on lattice basis reduction to solve the problem. For a general multivariate modular linear equation with short solution in the given bounded range, the new method outputs this short solution in polynomial time, with a high probability. When the number of unknowns is not too large （smaller than 68）, the probability is approximating 1. Experimental results show that Knapsack systems and Lu-Lee type systems are easily broken in polynomial time with this new method.