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One of the most important methods to protect and verify information that are exchanged over public communication channels in the existence of third party called antagonists is encryption. The stored or transmitted message is transformed in the encryption process to unreadable or gibberish form. The reverse process in which the intendent recipient can reveal the encrypted message content is called decryption. The encryption and decryption processes are achieved using secret keys that are exclusively exchanged between the sender and recipient. This method can be applied to any form of message such as audio, video, image or text data. The current work applies the well-known RSA algorithm for audio signal encryption and decryption. The performance of the presented algorithm has been tested via experimental implementation which show that the Cpestral Distance Measure (CD), Linear Predicative Code Measure (LPC) and Segmental Spectral Signal to Noise Ratio (SSSNR) reach to 6.8781, 4.9614 and -21.5563 dB respectively using Matlab simulations. The results on the presented technique validated that it is secure, reliable and efficient to be applied in secure audio communications as well as it performed high intelligibility of the recovered audio signal.

Now - a- days, the exchange of sensitive information, such as credit card numbers, over the internet is common practice. Protecting data and electronic systems is crucial to our way of living. Cryptography deals with the study of communication over a channel may not be secure and problems related with them. One such well known algorithm is RSA algorithm. This paper displays the classical RSA algorithm and modifies the work in generation of keys. There will be two assignments for the alphabets. Here the only interest is on messages with two letters.&nbsp

E-business security becomes an important issue in the development of technology, to ensure the safety and comfort of transactions in the exchange of information is privacy. This study aims to improve security in e-business systems using a hybrid algorithm that combines two types of keys, namely symmetric and asymmetric keys. Encryption and decryption of messages or information carried by a symmetric key using the simple symmetric key algorithm and asymmetric keys using the Rivest Shamir Adleman (RSA) algorithm. The proposed hybrid algorithm requires a high running time in the decryption process compared to the application of a single algorithm. The level of security is stronger because it implements the process of message encryption techniques with two types of keys simultaneously.

Cryptography, which involves the use of a cipher, describes a process of encrypting information so that its meaning is hidden and thus, secured from those who do not know how to decrypt the information. Cryptography algorithms come with the various types including the symmetric key algorithms and asymmetric key algorithms. In this paper, the authors applied the most commonly used algorithm, which is the RSA algorithm together with the Chaos system and the basic security device employed in the worldwide organizations which is the Data Encryption Standard (DES) with the objective to make a hybrid data encryption. The advantage of a chaos system which is its unpredictability through the use of multiple keys and the secrecy of the RSA which is based on integer factorization’s difficulty is combined for a more secure and reliable cryptography. The key generation was made more secure by applying the DES schedule to change the keys for encryption. The main strength of the proposed system is the chaotic variable key generator that chages the value of encrypted message whenever a different number of key is used. Using the provided examples the strength of security of the proposed system was tested and demonstrated.

Digital image is digital pictures on a two-dimensional plane which consists of pixels, where every pixels has Red, Green, Blue (RGB) with varying intensity depending on the image. In this thesis digital image is encrypted using hybrid algorithm Vigenere and RSA. Vigenere algorithm is a symmetric key algorithm which is a variety from Caesar algorithm where the similarity is in both of them are based on shifting the index of alphabet letters. RSA algorithm are based on the difficulty of factorizing large numbers that have 2 and only 2 factors (Prime numbers). The encryption process starts with getting the RGB intensity of each pixels from the image, then the RGB values are encrypted using Vigenere algorithm, after that RSA Algorithm encrypt those values, the values of RSA Algorithm encryption are limited so the value can be within the intervals of RGB values and the after limitation the values after being limited become the RGB values in the encrypted image. The decryption process is the inverse of encryption process, which enables the encrypted image to become the initial image before encryption. The program for encrypting and decrypting image are made using Java programming language with Netbeans IDE 8.2 software. The result of this implementation on image file donbass.jpg with the length of Vigenere key of 5 those are k1=144, k2=166 , k3=38 , k4=204 , k5=98, and RSA Algorithm keys are n=2201, e=1139, d=59, the results from the encrypted image is a visually very different image from the initial image. While in the decryption process, the encrypted image is able to be decrypted back to the initial image.

Among the modern methods of cryptographic information protection asymmetric algorithms is most widely used. A special place among them is occupied by RSA (Rivest-Shamir-Adleman) encryption algorithm, which recommended the use a number of international standards and recommendations. RSA cryptographic resistance is based on the difficulty of the task execution of multi-digit numbers factorization and is not an effective problem of compromising its software and hardware implementations. Currently the “fastest” ways of decomposition the big numbers into factors are methods of the general number field sieve (GNFS), the quadratic sieve (QS) algorithm and the elliptic curve factorization method (ECM). It is known that the basis of these methods are based on a number of fundamental relations of Fermat’s classical algorithm, proceeding from which it can be argued that the improvement of Fermat’s method can have an impact on reducing the computational complexity of modern factorization methods listed above. One of the ways to increase the efficiency of the improved Fermat's factoring method is a modification of existing or developing new algorithms of execution the algebraic operations with large numbers. Among these can be the operation of the modular division in procedures for advance sieving of test values X. A modified method of thinning test values in Fermat’s factoring algorithm is proposed, the main advantage of which is the refusal to perform complex arithmetic operations of modular division of large sequences and replacing them with the procedure of the modular division of small numbers., Среди современных методов криптографической защиты информации наибольшее применение получили так называемые асимметричные алгоритмы, к числу которых относится алгоритм RSA (Rivest-Shamir-Adleman). Его криптографическая стойкость основана на трудности выполнения задачи факторизации многоразрядных чисел. В основе большинства методов факторизации лежит ряд фундаментальных соотношений классического алгоритма Ферма. Одним из направлений повышения его эффективности является модифицирование существующих или разработка новых алгоритмов выполнения алгебраических операций с большими числами. К числу таких можно отнести операцию модульного деления в процедурах предварительного просеивания пробных значений Х. Предлагается модифицированный метод прореживания пробных значений в алгоритме факторизации Ферма, основным преимуществом которого является отказ от выполнения арифметически сложных операций модульного деления больших последовательностей и замена их на процедуру модульного деления малых чисел., Серед сучасних методів криптографічного захисту інформації найбільше застосування отримали так звані асиметричні алгоритми, до числа яких належить алгоритм RSA (Rivest-Shamir-Adleman). Його криптографічна стійкість визначається складнощами виконання завдання факторизації багаторозрядних чисел. В основі більшості методів факторизації лежить ряд фундаментальних співвідношень класичного алгоритму Ферма. Одним з напрямків підвищення його ефективності є модифікування існуючих або розроблення нових алгоритмів виконання алгебраїчних операцій з великими числами. До числа таких можна віднести операцію модульного ділення в процедурах попереднього проріджування пробних значень Х. Пропонується модифікований метод проріджування пробних значень в алгоритмі факторизації Ферма, основною перевагою якого є відмова від виконання арифметично складних операцій модульного поділу великих послідовностей і заміна їх на процедуру модульного розподілу малих чисел.

Security is one of the most important concern to the information and data sharing for companies, banks, organizations and government facilities. RSA is a public cryptographic algorithm that is designed specifically for authentication and data encryption. One of the most powerful reasons makes RSA more secure is that the avoidance of key exchange in the encryption and decryption processes. Standard RSA algorithm depends on the key length only to protect systems. However, RSA key is broken from time to another due to the development of computers hardware such as high speed processors and advanced technology. RSA developers have increased a key length or size of a key periodically to maintain a high security and privacy to systems that are protected by the RSA. In this paper, a method has been designed and implemented to strengthen the RSA algorithm by using multiple public and private keys. Therefore, in this method the security of RSA not only depends on the key size, but also relies on the multiplicity of public and private keys.

Security algorithms like RSA are becoming increasingly important for communications to provide companies, organizations, and users around the world, secure applications who rely heavily on them in their daily work. Security algorithms use different acquaintances among companies which might belong to various countries or even cities. Such data should essentially be encrypted to make sure that there is security in transportation. Thus, the current research paper leads to the novel system of security for the safe transfer of data. This paper examines the general principles of encryption and focuses on the development of RSA and the complexity of the encryption key so that it becomes more secure in the applications used. In this project, we will work on the RSA algorithm by adding some complexity to the 3keys (3k). This addition will increase the security and complexity of the algorithm's speed while maintaining encryption and decryption time. The paper also presents an approach by means of public key encryption to enhance cryptographic security. Moreover, double security is provided by the algorithm of RSA. This novel RSA algorithm was investigated in MATLAB. Numerical results for the various parameters such as Mean Square Error (MSE), correlation and Bit Error Ratio (BER) were implemented for the encryption of the message. The experimental results demonstrated that the proposed algorithm for 3 keys has small error rate in the retrieval of the encoded text.

We measure the popularity of cryptographic libraries in large datasets of RSA public keys. We do so by improving a recently proposed method based on biases introduced by alternative implementations of prime selection in different cryptographic libraries. We extend the previous work by applying statistical inference to approximate a share of libraries matching an observed distribution of RSA keys in an inspected dataset (e.g., Internet-wide scan of TLS handshakes). The sensitivity of our method is sufficient to detect transient events such as a periodic insertion of keys from a specific library into Certificate Transparency logs and inconsistencies in archived datasets. We apply the method on keys from multiple Internet-wide scans collected in years 2010 through 2017, on Certificate Transparency logs and on separate datasets for PGP keys and SSH keys. The results quantify a strong dominance of OpenSSL with more than 84% TLS keys for Alexa 1M domains, steadily increasing since the first measurement. OpenSSL is even more popular for GitHub client-side SSH keys, with a share larger than 96%. Surprisingly, new certificates inserted in Certificate Transparency logs on certain days contain more than 20% keys most likely originating from Java libraries, while TLS scans contain less than 5% of such keys. Since the ground truth is not known, we compared our measurements with other estimates and simulated different scenarios to evaluate the accuracy of our method. To our best knowledge, this is the first accurate measurement of the popularity of cryptographic libraries not based on proxy information like web server fingerprinting, but directly on the number of observed unique keys.

The RSA algorithm is one of the most commonly used efficient cryptographic algorithms. It provides the required amount of confidentiality, data integrity and privacy. This paper integrates the RSA Algorithm with round-robin priority scheduling scheme in order to extend the level of security and reduce the effectiveness of intrusion. It aims at obtaining minimal overhead, increased throughput and privacy. In this method the user uses the RSA algorithm and generates the encrypted messages that are sorted priority-wise and then sent. The receiver, on receiving the messages decrypts them using the RSA algorithm according to their priority. This method reduces the risk of man-in-middle attacks and timing attacks as the encrypted and decrypted messages are further jumbled based on their priority. It also reduces the power monitoring attack risk if a very small amount of information is exchanged. It raises the bar on the standards of information security, ensuring more efficiency.

This paper describes basic principles of data protection using the RSA algorithm, as well as algorithms for its calculation. The RSA algorithm is implemented on FPGA integrated circuit EP4CE115F29C7, family Cyclone IV, Altera. Four modules of Montgomery algorithm are designed using VHDL. Synthesis and simulation are done using Quartus II software and ModelSim. The modules are analyzed for different key lengths (16 to 1024) in terms of the number of logic elements, the maximum frequency and speed.

RSA Cryptosystem is considered the first practicable secure algorithm that can be used to protect information during the communication. The significance of high security and efficient implementations of RSA have formed the base of many cryptographic engineering researches. In fact, the implementation of RSA Cryptosystem is heavily based on modular arithmetic and exponentiation involving large prime numbers. In this paper, we propose an efficient FPGA design and architecture for RSA cryptosystem using ALTERA FPGA Hardware Kit. The proposed design comprises six levels: random two prime numbers, parallel multiplication of the prime numbers and their decremented values, get encryption key, get decryption key, encryption and decryption levels. As the modular multiplication is considered as the heart of RSA computations, Interleaved Algorithm was particularly chosen as an efficient solution to speed up the modular multiplication. The experimental part of this work has been synthesized for both ALTERA Cyclone IV EP4CE115F29C7 and VERTIX VII VC707 FPGA kits and resulted in a maximum frequencies of 15.725 MHz, 17.629 MHz respectively. These findings make our design comparable and a good choice for efficient RSA Cryptoprocessor design. The results for the FPGA implementation for EC design using these curves is also proposed in this paper.

In many research works, there has been an orientation to studying and developing many of the applications of public-key cryptography to secure the data while transmitting in the systems, In this paper we present an approach to encrypt and decrypt the message text according to the ASCII(American Standard Code for Information Interchange) and RSA algorithm by converting the message text into binary representation and dividing this representation to bytes(8s of 0s and 1s) and applying a bijective function between the group of those bytes and the group of characters of ASCII and then using this mechanism to be compatible with using RSA algorithm, finally, Java application was built to apply this approach directly., for any notes and queries please contact via: msma776@gmail.com, http://airccse.org/journal/ijcis/current2015.html