The RSA cryptosystem, invented by Ron Rivest, Adi Shamir and Len Adleman was first publicized in the August 1977 issue of Scientific American. The security level of this algorithm very much depends on two large prime numbers. To check the primality of large number in personal computer is huge time consuming using the best known trial division algorithm. The time complexity for primality testing has been reduced using the representation of divisors in the form of 6n±1. According to the fundamental theorem of Arithmetic, every number has unique factorization. So to check primality, it is sufficient to check if the number is divisible by any prime below the square root of the number. The set of divisors obtained by 6n±1 form representation contains many composites. These composite numbers have been reduced by 30k approach. In this paper, the number of composites has been further reduced using 210k approach. A performance analysis in time complexity has been given between 210k approach and other prior applied methods. It has been observed that the time complexity for primality testing has been reduced using 210k approach.

Different optimization techniques have been used to solve Sudoku. Zong Woo Geem have applied harmony search in Sudoku to get better result. He has taken a Sudoku and time complexity has been optimized by different values of parameters. But, he has not given way of solution in details. He has also not given any idea to recognize the level of Sudoku. In this paper, an algorithm has been proposed based on harmony search to solve and identify the Sudoku efficiently. It has been observed that time complexity i.e. the maximum number of iteration has been reduced by choosing appropriate parameter values. The level of Sudoku has also been identified using probability metric. Finally, the number of iterations has been calculated with different values of parameters and the level of different Sudoku has been identified.

Clustering is partitioning of data set into subsets (clusters), so that the data in each subset share some common trait. In this paper, an algorithm has been proposed based on Fuzzy C-means clustering technique for prediction of adsorption of cadmium by hematite. The original data elements have been used for clustering the random data set. The random data have been generated within the minimum and maximum value of test data. The proposed algorithm has been applied on random dataset considering the original data set as initial cluster center. A threshold value has been taken to make the boundary around the clustering center. Finally, after execution of algorithm, modified cluster centers have been computed based on each initial cluster center. The modified cluster centers have been treated as predicted data set. The algorithm has been tested in prediction of adsorption of cadmium by hematite. The error has been calculated between the original data and predicted data. It has been observed that the proposed algorithm has given better result than the previous applied methods.

Visual cryptography is a method for protecting image-based secrets that has a computation-free decoding process. In this technique, numbers of shares have been generated from one image. The shares are sent through any channel to the receiver and the receiver can again produce original image by stacking all the shares in proper order. But, this method wastes a lot of bandwidth of the network. The techniques of generating shares have been used in several existing methods which are not unique. The different methods have been used in different types of images like binary, gray and color images. In this paper, a block based symmetry key visual cryptography algorithm has been proposed to convert image in encrypted form and decrypt the encrypted image into original form. The symmetric key has been generated from a real number. The encryption and decryption algorithm have been designed based on symmetry key. The algorithm with key has been used to encrypt image into single share and decrypt the single share into original image. The real number has been used to form the key may be predefined or may be sent by secure channel to the receiver. The proposed algorithm can be applied to any type images i.e. binary, gray scale and color images. A comparison has been made of the proposed algorithm with different existing algorithms like Ceaser cipher, transpose of matrix, bit comp, and transposition cipher based on the performance. The pixels distributed in original and share images have also been tested. Finally, it has shown that breaking of security level of proposed algorithm i.e. to guess the real number is huge time consuming.

A human eye can detect a face in an image whether it is in a digital image or also in some video. The same thing is highly challenging for a machine. There are lots of algorithms available to detect human face. In this paper, a technique has been made to detect and locate the position of human faces in digital images. This approach has two steps. First, training the artificial neural network using Levenberg–Marquardt training algorithm and then the proposed algorithm has been used to detect and locate the position of the human faces from digital image. The proposed algorithm has been implemented for six color spaces which are RGB, YES, YUV, YCbCr, YIQ and CMY for each of the image formats bmp, jpeg, gif, tiff and png. For each color space training has been made for the image formats bmp, jpeg, gif, tiff and png. Finally, one color space and particular image format has been selected for face detection and location in digital image based on the performance and accuracy.