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Given Y ∈ R m× and A ∈ R m×n , the multiple measurement vector (MMV) problem aims to recover the support of the K -row sparse matrix X from Y = AX + E. In this paper, we present a sufficient condition for exact support recovery of K -row sparse matrices via the orthogonal matching pursuit for MMV (OMPMMV) algorithm in the noisy case. Furthermore, in the noiseless case, our proposed condition is optimal.INDEX TERMS Compressed sensing, multiple measurement vector, greedy algorithm.

In many cryptographic applications, random numbers and pseudorandom numbers are required. Many cryptographic protocols require using random or pseudorandom numbers at various points, e.g., for auxiliary data in digital signatures or challenges in authentication protocols. In NIST SP800-22, the focus is on the need for randomness for encryption purposes and describes how to apply a set of statistical randomness tests. These tests can be used to evaluate the data generated by cryptographic algorithms. This paper will study the fast software implementation of the serial test and the approximate entropy test and propose two types of fast implementations of these tests. The first method is to follow the basic steps of these tests and replace bit operations with byte operations. Through this method, compared with the implementation of Fast NIST STS, the efficiency of the serial test and approximate entropy test is increased by 2.164 and 2.100 times, respectively. The second method is based on the first method, combining the statistical characteristics of subsequences of different lengths and further combining the two detections with different detection parameters. In this way, compared to the individual implementation of these tests, the efficiency has been significantly improved. Compared with the implementation of Fast NIST STS, the efficiency of this paper is increased by 4.078 times.

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