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Information security has become a significant concern, and the protection of images transmitted over the Internet is vital, which requires a high level of security. The information in these images has been used without permission and, therefore, will have serious consequences, and the images can be secured in several ways. Data encryption and decryption have recently received much attention and development. Strong encryption and decryption is required, which is incredibly difficult to crack. In this paper, an encryption environment consisting of triple encryption methods was used to create a new encryption system, which depends on several stages, including the step involving the process of creating the key using the RSA algorithm and then using this generated key with the same RSA algorithm to encrypt the image, in the second stage using a method "zig_zag" in order to encrypt the image again based on the encrypted pictures generated from the first stage, in the third stage, encrypt the image generated from the second stage using the 2D CAT method. As for the setting of retrieval of the original photos using triple decryption methods in a reverse way, the idea was returned without losing its data. The image quality was excellent.

Currently encryption methods are much more sophisticated , among them the most used is the RSA algorithm, created by Rivest, Shamir, Adleman pblished in 1977 in the journal Scientific American, based on prime numbers of great magnitude, the which uses the model of a public and a private key (asymmetric encryption) . The reliability offered by the RSA algorithm allowed Phil Zimmerman in 1991, develop PGP (Pretty Good Privacy) which is an encryption algorithm that works easily on home computers. PGP uses classical cryptography concepts and combines them with the RSA algorithm . In most classical ciphers, the algorithms developed are based on mathematical foundations, for example, modular arithmetic, the fundamental theorem of arithmetic and its applications to prime numbers, such as the Euler function and the Chinese remainder theorem, among others. others. For the transposition encryption system, an encryption and decryption algorithm can be determined whose mathematical basis is based on matrix algebra .

Network safety has become an important issue in recent years. Encryption has been developed as a solution and plays an important role in the security of information systems. Many methods are required to secure the shared data. The advanced internet, networking firms, health information and the cloud applications have significantly increased our data every minute. The current work focuses on cryptography to provide the protection for sensitive data that exchanged between personal users, companies, organizations, or in the cloud applications and others during the transfer of data across the network. Firstly, Data sent from sender to network receiver must be encrypted using the cryptographic algorithm. Secondly, the recipient shows the original data using the decryption technique. This paper presents three encrypting algorithms such as AES, RSA and hybrid algorithms, and their efficiency is compared based on the analysis of the time. Results of the experiments show that the hybrid algorithm is better in term of security.

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

This paper proposes a secure offline electronic (e-) payment scheme by adopting Schnorr's untraceable blind signature (BS). Thereby, to satisfy the essential security requirements of e-payment systems, it requires much more simple computations and becomes more practical than many existing schemes. Other considerations are: to prevent the forgery of e-coin, the Bank is only the lawful entity to produce the valid e-coin; and others can verify its correctness. To confirm no swindling, the e-coin owner also sticks her private signing key with the e-coin before spending it as the payment. Hence, through the commitment with challenge-response of Schnorr's BS, the merchant can verify the spent e-coin, and the trusted authority can identify the dishonest spender if multiple spending occurs. Moreover, it embeds three distinct information of date, namely expiration, deposit, and transaction dates with every e-coin. Thereby, it minimizes the size of the Bank's database, correctly calculates the interest of the e-coin, and helps in arbiter if multiple spending, respectively. Finally, it evaluates the performance and analyzes essential security requirements of the proposed scheme, plus studies a comparison with existing ones.

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.

In literature, there are a number of cryptographic algorithms (RSA, ElGamal, NTRU, etc.) that require multiple computations of modulo multiplicative inverses. In this paper, we describe the modulo operation and we recollect the main approaches to computing the modulus. Then, given a and n positive integers, we present the sequence (zj)j≥0, where zj=zj−1+aβj−n, a&lt, n and GCD(a,n)=1. Regarding the above sequence, we show that it is bounded and admits a simple explicit, periodic solution. The main result is that the inverse of a modulo n is given by a−1=⌊im⌋+1 with m=n/a. The computational cost of such an index i is O(a), which is less than O(nlnn) of the Euler’s phi function. Furthermore, we suggest an algorithm for the computation of a−1 using plain multiplications instead of modular multiplications. The latter, still, has complexity O(a) versus complexity O(n) (naive algorithm) or complexity O(lnn) (extended Euclidean algorithm). Therefore, the above procedure is more convenient when a&lt, &lt, n (e.g., a&lt, lnn).

Secure data transmission is a challenging and fundamental aspect nowadays. Secure and nonvulnerable transmission of authenticated data is ensured by using cryptography and steganography methods. Advancement in technology leads to a new cryptographic algorithm each day. Recent advancement has led to a new technique called DNA cryptography. In this paper, the RSA algorithm, DNA cryptography, and steganography methods are followed to encrypt the plain text by assuring triple security. This combination will produce a more robust, more secure algorithm that is hard for the intruder to decrypt the message.

A type of distributed and self-regulating network is the wireless sensor network (WSN). The sensor nodes have limited computing capabilities, memory, battery power are needed to ensure a strong security design. In this paper, an adaptive cryptographic scheme for WSN that is operating on routing ad hoc on-demand vector routing (AODV) protocol. The adaptive term refers to the adopted mechanism between heavy and light asymmetric cryptography techniques of RSA. The heavy technique adopts the complete version of RSA algorithm, while the light one considers a reduced complexity version. This is to control the security operation over the included nodes even with low power ratio. In various case studies, the proposed scheme is checked and the result obtained shows the high efficiency of results in terms of protection guarantee.

Yüksek Lisans Tezi, Matematikte zor problem olarak kabul edilen problemlerden Çarpanlara Ayırma Probleminin zorluğu verilen bileşik sayının asal çarpanlarının büyüklüğüne bağlıdır. Daha açık bir ifadeyle, bu problemin zorluğu üzerine dayanan kriptosistemin güvenilir olabilmesi için çarpan olarak kullanılan asal sayıların yeteri kadar büyük olması gerekmektedir. Bu durumda yeteri kadar büyüklükte asal sayı üretme problemi karşımıza çıkmaktadır. Literatürde, büyük sayıların asal olup olmadığını belirlemek için çeşitli asallık testleri önerilmiştir ve bazıları günümüzde pratik olarak kullanılmaktadır. Bu tez çalışmasında literatürde yer alan olası asallık testleri ve kesin asallık testleri ayrıntılı olarak incelenmiş ve örneklerle desteklenmiştir. Olası asallık testlerinin çalışma zamanları esas alınarak performans analizleri yapılmış ve karşılaştırmaları sayısal verilerle sunulmuştur. Olası asallık test algoritmalarının hata oranları ve karmaşıklıkları verilerek bir karşılaştırma sunulmuştur. Ek olarak bu tez çalışmasında, güvenliği çarpanlara ayırma probleminin zorluğuna dayanan ve günümüzde pratik kullanımda çok önemli bir yere sahip olan RSA şifreleme algoritması ayrıntılı olarak incelenmiştir. Bu tezin ekler bölümünde, tezde verilen bazı algoritmaların ve asallık testlerinin C++ programlama dilindeki kodları sunulmuştur., The hardness of the Integer Factorization Problem that is considered as one of the hard problems in mathematics depends on the sizes of the prime factors of the given odd composite number. More precisely, the prime factors must be large enough so that cryptosystem whose security is based on the difficulty of this problem can be reliable. In this case, we encounter the problem of finding sufficiently large prime numbers. In the literature, to determine whether large odd numbers are prime numbers, primality test algorithms have been proposed, and some of them have been applied in practical life. In this thesis, the probabilistic and deterministic primality test algorithms are studied in detail, and several concrete examples are presented. The performance analyses of the probabilistic primality tests are performed by considering the running times. Moreover, a comparison of these tests is presented according to their error probability and time complexities. In addition, we investigate the RSA encryption algorithm whose reliability is based on the hardness of the integer factorization problem and which has a significant role in practical use today. The appendix provides the implementation codes of some algorithms and primality tests in the C++ programming language.

To send text messages free of charge using an existing mobile number, you can use this system like SMS messenger and install it on your mobile device. This apk is an application that enables you to text and sends small images to other this apk’s users without charge. To send a secure message, secure sessions must exist between the sending device and all the recipient’s devices. Asymmetric key cryptography algorithm RSA is used for encryption and decryption of the message. The user can obtain the security of text messages using RSA. This system provides a secure message on the mobile phone. Every SMS packet contains 140 bytes of effective data. Mobile users send short messages to the short message center through mobile terminals, and then the short message center transmits these short messages to target users.

Several ways to perform data encryption have been found, and one of the functions involved in standard algorithms such as RSA is the modular exponentiation. Basically, the RSA algorithm uses some properties of modular arithmetic to cipher and decipher plain text, with a certain performance dependence on text lengths. The growth in computing capacity has created the need to use robust systems that can perform calculations with significantly large numbers and the formulation of procedures focused on improving the speed to achieve it. One of these is the M-ary algorithm for the execution of the modular exponential function. This paper describes an implementation of this algorithm in reprogrammable hardware (FPGA) to evaluate its performance.The first section of this work introduces the M-ary algorithm. The second section uses block description for implementation understanding. The third section shows the results in time diagrams, and finally, the last section conclusions. Se han encontrado diversas formas de realizar cifrado de datos, y una de las funciones involucradas en algoritmos estándar como el RSA es la exponencial modular. Básicamente, el algoritmo RSA utiliza algunas propiedades de la aritmética modular para cifrar y descifrar textos planos, con cierta dependencia en la longitud del texto. El crecimiento en la capacidad de cómputo ha creado la necesidad de utilizar sistemas robustos que puedan realizar cálculos con números significativamente grandes, y la formulación de procedimientos enfocados en mejorar la velocidad para lograrlo. Uno de éstos es el algoritmo M-ary para la ejecución de la función exponencial modular. Este artículo describe una implementación de este algoritmo en hardware reprogramable (FPGA) para evaluar su desempeño.La primera sección introduce el algoritmo M-ary. La segunda, usa descripción en bloques para comprender la implementación. La tercera, muestra los resultados en diagramas de tiempo, y finalmente, la última sección expone conclusiones.

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.

This paper aims to provide security of data in the Cloud using Multiplicative Homomorphic Approach. Encryption process is done with RSA algorithm. In this RSA algorithm, Shor’s algorithm is used for generating Public key Component, which enhances the security. Shor’s algorithm plays as important role in generating public key. Plain Text Message is encrypted with Public Key to generate Cipher Text and for decryption Chinese Remainder Theorem (CRT) is used to speed up the computations. By doing so, it shows how the CRT representation of numbers in Zn can be used to perform modular exponentiation about much more efficiently using three extra values pre-computed from the prime factors of n. Hence, security is enhanced in the cloud provider.

RSA Rivest-Shamir-Adleman is an algorithm used by modern computers to encrypt and decrypt messages. The purpose of the paper is how to produce two different keys. This is also called public key cryptography, because one of the keys can be given to anyone. In this paper also represent how to separate unwanted character by using Linux command. Soe Moe Myint | Moe Moe Myint | Aye Aye Cho "A Study of RSA Algorithm in Cryptography" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26749.pdf

Genetski algoritmi su poznata i često korištena heuristička metoda za rješavanje optimizacijskih problema. Tema rada je primjena genetskih algoritama na generiranje velikih prostih brojeva koji imaju poseban značaj u kriptografiji. Dan je uvod u te- oriju prostih brojeva te metode koje se koriste za provjeru prostosti nekoga (velikog) broja. Prikazana je implementacija genetskog algoritma za generiranje prostih brojeva uz prikladan prikaz rješenja i genetske operatore. Rezultati su analizirani i prikazani grafički za različite parametre genetskog algoritma. Genetic algorithms are a well-known and frequently used heuristic method for sol- ving optimization problems. The theme of the paper is the application of genetic al- gorithms for generating large prime numbers that have special significance in crypto- graphy. An introduction to the theory of prime numbers and the methods used to check the primality of a large number are shown. The implementation of a genetic algorithm for generating prime numbers is presented with a convenient representation and gene- tic operators. The results were analyzed and graphically presented for different genetic algorithm parameters.

Günümüzde, bilişim teknolojilerinin gelişmesiyle birlikte haberleşme ve bilgi güvenliğinin sağlanması için şifrelemenin önemi giderek artmaktadır. Özellikle internet teknolojisinin gelişmesiyle birlikte veri güvenliğinin sağlanması için birçok şifreleme algoritmaları kullanılmaktadır. Şifreleme algoritmaları simetrik ve asimetrik olmak üzere iki başlık altında incelenmektedir. Bu çalışmada ise simetrik ve asimetrik şifreleme algoritmalarının genel özelliklerine yer vermekle birlikte literatürde önemli bir yere sahip asimetrik şifreleme algoritmalarından biri olan RSA algoritması incelenerek RSA algoritmasının şifreleme yöntemleri üzerindeki etkisi analiz edilmiştir. RSA algoritmasının yapısı, genel özellikleri, avantajı ve dezavantajı hakkında bilgilere yer verilmiştir., Nowadays, with the development of information technologies, the importance of encryption for communication and information security is gradually increasing. Especially internet technology has been developed and many encryption algorithms have been used to provide data security. Encryption algorithms are examined under two headings as symmetric and asymmetric. In this study, the general properties of symmetric and asymmetric encryption algorithms are given and the effect of the RSA algorithm on the encryption methods is analyzed by examining the RSA algorithm which is one of the asymmetric encryption algorithms in the literature. The structure, general properties, advantages and disadvantages of the RSA algorithm are given.

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.

International audience; This work proposes an extension of the well-known random sequential adsorption (RSA) method in the context of non-overlapping random mono-and polydisperse ellipsoidal inclusions. The algorithm is general and can deal with inclusions of different size, shape and orientation with or without periodic geometrical constraints. Specifically, polydisperse inclusions, which can be in terms of different size, shape, orientation or even material properties, allow for larger volume fractions without the need of additional changes in the main algorithm. Unit-cell computations are performed by using either the fast Fourier transformed-based numerical scheme (FFT) or the finite element method (FEM) to estimate the effective elastic properties of voided particulate microstructures. We observe that an isotropic overall response is very difficult to obtain for random distributions of spheroidal inclusions with high aspect ratio. In particular, a substantial increase (or decrease) of the aspect ratio of the voids leads to a markedly anisotropic response of the porous material, which is intrinsic of the RSA construction. The numerical estimates are probed by analytical Hashin-Shtrikman-Willis (HSW) estimates and bounds.

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.

Several ways to perform data encryption have been found, and one of the functions involved in standard algorithms such as RSA is the modular exponentiation. Basically, the RSA algorithm uses some properties of modular arithmetic to cipher and decipher plain text, with a certain performance dependence on text lengths. The growth in computing capacity has created the need to use robust systems that can perform calculations with significantly large numbers and the formulation of procedures focused on improving the speed to achieve it. One of these is the M-ary algorithm for the execution of the modular exponential function. This paper describes an implementation of this algorithm in reprogrammable hardware (FPGA) to evaluate its performance. The first section of this work introduces the M-ary algorithm. The second section uses block description for implementation understanding. The third section shows the results in time diagrams, and finally, the last section conclusions. Resumen Se han encontrado diversas formas de realizar cifrado de datos, y una de las funciones involucradas en algoritmos estándar como el RSA es la exponencial modular. Básicamente, el algoritmo RSA utiliza algunas propiedades de la aritmética modular para cifrar y descifrar textos planos, con cierta dependencia en la longitud del texto. El crecimiento en la capacidad de cómputo ha creado la necesidad de utilizar sistemas robustos que puedan realizar cálculos con números significativamente grandes, y la formulación de procedimientos enfocados en mejorar la velocidad para lograrlo. Uno de éstos es el algoritmo M-ary para la ejecución de la función exponencial modular. Este artículo describe una implementación de este algoritmo en hardware reprogramable (FPGA) para evaluar su desempeño. La primera sección introduce el algoritmo M-ary. La segunda, usa descripción en bloques para comprender la implementación. La tercera, muestra los resultados en diagramas de tiempo, y finalmente, la última sección expone conclusiones.

Kriptografija je grana primijenjene matematike koja se bavi sigurnošću prijenosa poruka komunikacijskim kanalom. RSA je asimetrični algoritam s javnim ključem i danas je jedan od najpoznatijih kriptografskih algoritama. Zbog asimetričnosti, osjetno je sporiji i stoga se ne koristi za kriptiranje većih sadržaja. Primjenjuje se kod razmjene zajedničkog tajnog ključa kojim se onda kriptira veći sadržaj. Funkcije kriptiranja i dekriptiranja e_K i d_K su jednosmjerne te pripadaju modularnoj aritmetici. Sigurnost ovog kriptosustava temelji se na složenosti faktorizacije velikih brojeva i jednosmjernosti funkcija e_K i d_K. Ključno je na pravilan način odabrati parametre koji čine tajni i javni ključ. Neoprezan korisnik može puno olakšati napadaču probijanje sustava ako ne prati preporuke za odabir parametara. Kriptoanaliza je grana primijenjene matematike koja se bavi otkrivanjem šifri i postupcima „probijanja“ zaštićenih podataka. Postoji mnogo poznatih vrsta napada na RSA kriptosustav. Svaki od njih se u konačnici oslanja na takav splet okolnosti u kojem je korisnik odabrao lošu kombinaciju parametara. RSA još uvijek nije probijen te ga zasad možemo smatrati sigurnim, iako za to ne postoji matematički dokaz. Cryptography is a branch of applied mathematics whose main focus represents safeness of messages sent through the communication channel. RSA is an asymmetric public key algorithm and it is one of the most famous cryptographic algorithms nowadays. Due to the asymmetry, it is considerably slower and therefore not used for encryption of larger contents. It is applied in the secret key exchange, which is then used to encrypt larger content. Encryption and decryption functions, e_K and d_K, are one-way functions that are based on modular arithmethics. Safeness of this cryptosystem is based on complexity of large number factorization and on the fact that e_K and d_K are one-way functions. The key is to properly choose the parameters that form the secret and public key. An unwary user can make the cracking much easier for the attacker if he does not follow the recommendations when choosing parameters. Cryptoanalysis is a branch of applied mathematics that deals with the detection of ciphers and methods of cracking encrypted data. There are many common methods for attacking the RSA cryptosystem, but in the end, all of them rely on a combination of circumstances in which the user has chosen a poor set of parameters. RSA still hasn’t been cracked, and for now, it can be considered safe, even though there is no mathematical proof of that.

Visible light communication systems are rapidly growing research areas with wide applications ranging from illumination and data communication. To achieve high data rates in such systems, a number of techniques have been employed such as equalization of transmission signals, deployment of complex data modulation and the use of multiple input multiple output (MIMO) systems. However, security in wireless telecommunication systems is a common concern. This paper proposes a secure MIMO-VLC system that relies on the position of the user by incorporating a new modified version of the Rivest-Shamir-Adleman (RSA) technique for encrypting the transmitted data in the media access control MAC layer. The performance of the positioning method is evaluated showing a positioning accuracy of less than 5 cm for a signal-to-noise ratio of 15 dB. Furthermore, the ability of the proposed system to control the size of the encrypted cell, depending on the application environment, is demonstrated. 1983-2012 IEEE. Manuscript received May 11, 2017; revised July 20, 2017; accepted September 23, 2017. Date of publication October 8, 2017; date of current version November 27, 2017. This work was supported in part by the Northumbria University, U.K., in part by the Azzaytuna University, Libya, and in part by the the Ministry of Higher Education of Libya. (Corresponding author: Farag Ibrahim Khalifa Mousa.) F. Mousa, K. Busawon, A. Bouridane, and R. Binns are with the Faculty of Engineering and Environment, Northumbria University, Newcastle Upon Tyne NE1 8ST, U.K. (e-mail: farag.mousa@northumbria.ac.uk; krishna.busawon@ northumbria.ac.uk; ahmed.bouridane@northumbria.ac.ukk; richard.binns@ northumbria.ac.uk). Scopus

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.

This bachelor thesis focuses on the RSA algorithm and it's use in electronic communication. The RSA algorithm is curently one of the most widely used asymmetric encryption algorithms. It was first publicly described in 1977 by the mathematicians Ron Rivest, Adi Shamir, and Leonard Adleman. It's the first algorithm that is suitable for both electronic signature and public key encryption. The theoretical part explains all related concepts of cryptography. The basic operating principle of the algorithm is described in specific simplified example. It also includes a description of public key encryption and a list of institutions, which use digital signature to verify authenticity of the sender. The practical part focuses on a questionnaire survey, which investigates the awareness level of internet banking users in term of security of using internet banking and following the security policy recommended by banks. The results are analysed and evaluated at the end of the thesis.

In this work a numerical model capable to predict the electromagnetic response of railway ballast aggregates under different physical conditions has been calibrated and validated by a simulation-based approach. The ballast model is based on the main physical and geometrical properties of its constituent material and it is generated by means of a random-sequential absorption (RSA) approach. A finite-difference time-domain (FDTD) simulator is then employed to calculate the ground-penetrating radar (GPR) signal response to the scenario. The calibration of the model has been performed by taking into account the main physical properties and the grain size characteristics of both the reference ballast material and a fine-grained pollutant material, namely, an A4 soil type material, according to the AASHTO soil classification. The synthetic GPR response has been generated by using the gprMax freeware simulator. Several scenarios have been considered, which in turn were reproduced in laboratory environment and used for the validation of the model. Promising results have demonstrated the high potential of such approach in characterizing the simulated response of complex coarse-grained heterogeneous materials.

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. 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.

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

Симетричні криптосистеми характеризуються тим, що ключі для шифрування та дешифрування інформації збігаються або ж один можна обчислити при наявності іншого.

Blind Signature were introduced by Chaum. In this scheme, a signer can “sign” a document without knowing the document contain. This is particularly important in electronic voting. CryptO-0N2 is an electronic voting protocol which is development of CryptO-0N. During its development this protocol has not been furnished with the requirement of blind signature, so the choice of voters can be determined by counting center. In this paper will be presented of implementation of blind signature using RSA algorithm., {"references":["","Ari Juels, M.Luby and R. Ostrovsky, \"Security of Blind Siganture\n(Extended Abstract),\" in Burton S. Kaliski Jr., editor, Advanced in\nCryptology – CRYPTO 97, vol. 1294 of Lecture Notes in Computer\nScience, Santa Barbara, CA, USA, August 17 – 21: Springer, Berlin,\nGermany, 1997, pp. 150 – 164.","Rong-Jaye Chen, \"Blind Signature and Their Application\",\nhttp://people.cs.nctu.edu.tw/~rjchen/Crypto2010/Blind_Signature.pdf\nlast access 20 April 2013.","E.R. Agustina, P.Y. Prakasa, CryptO-0N: Protocol Solution for Secure\nUbiquitous e-Voting, CryptO-0N: Solusi Protokol untuk Secure\nUbiquitous e-Voting (Translation Proceeding), Seminar Riset Teknologi\nInformasi (SRITI),2009.","P.Y Prakasa, I. Budiarso, E.R. Agustina, Secure e-Election Application\nby Utilizing Cryptographic Function and Fingerprint Technology for\nSupporting e-Democracy, Aplikasi Secure e-Election dengan\nMemanfaatkan Fungsi Kriptografi dan Teknologi Fingerprint untuk\nMendukung e-Democracy (Translation Proceeding), Seminar Nasional\nInformatika UPN Veteran Jogjakarta, 2009.","P.Y Prakasa, Z. Suhardono, E.R Agustina, Logic Approach Analysis of\nCryptO-0N Protocol, Analisis Pendekatan Logic pada Protokol CryptO-\n0N (Translation Journal),InfoKripto, 2012.","E.R. Agustina, P.Y. Prakasa, B. Smith, \"Analysis of CryptO-0N Protocol\nusing Boyd and Mao Logic Approach,\"2011, unpublished.","P.Y. Prakasa, \"Application Engineering Secure e-Voting with CryptO-\n0N2 Protocol Implementation for Electronic Election, Rancang Bangun\nAplikasi Secure e-Voting dengan Implementasi Protocol CryptO-0N2\nuntuk Pemilihan Umum Elektronis\", Tesis Magister Universitas\nGunadarma, 2012.","P.Y. Prakasa, E.R. Agustina, Security Optimization System Secure e-\nVoting for Supporting Electronic Election, Optimalisasi Keamanan\nSistem Secure e-Voting untuk Mendukung Pemilihan Umum Elektronik\n(Translation Journal), Jurnal Sandi, 2012.","P.Y. Prakasa, E.R. Agustina, KIOSK Electronic Voting with Certificate\nDigital Implementation for Supporting Electronic Election Security,\nKIOSK Electronic Voting dengan Implementasi Sertifikat Digital untuk\nPengamanan Pemilihan Umum Elektronis, 2013, submitted for\npublication.\n[10] A.J. Menezes, P.C van Oorschot, S.A Vanstone, Handbook of Applied\nCryptography (Book Style), CRC Press. Boca Raton, 1997."]}

Komuniciranje je velik del našega vsakdana, s tem pa se pokaže tudi potreba po varnem komuniciranju. Ljudje vsakodnevno uporabljamo bankomate, trgovske kartice popustov, pošiljamo elektronsko pošto, plačujemo račune preko spletnega bančništva, preverjamo in urejamo osebne podatke preko spletnih strani državnih uprav in podobno, pri tem pa se ne sprašujemo kam in kako pošiljamo naše osebne podatke. Vsak tak sistem temelji na svojem kriptosistmu, ki omogoča varno komunikacijo, brez, da bi njegovi uporabniki morali za karkoli skrbeti. Eden najbolj zanesljivih je RSA kriptosistem, ki je podrobneje predstavljen v diplomskem delu. Teorija števil, ki stoji za RSA kriptosistemom, obravnava področja praštevil, deljivosti in kongruenc, ki jih predstavimo v uvodu diplomskega dela. Sledijo jim drugi matematični pojmi, ki so tesno povezani z RSA: testi praštevilskosti, generiranje velikih praštevil, faktorizacija števil in diskretni logaritmi. Za konec so predstavljeni nekateri bolj znani napadi na RSA kriptosistem, v okviru katerih preverimo kdaj je RSA ranljiv in kaj so njegove šibke točke. Communication is a big part of our everyday lives, and we can clearly see the need for secure communication. We daily use ATMs, discount cards and e-mails, we pay bills via online banking systems, and manage personal information through the national administration websites, but we don’t ask ourselves where and how we send our personal data. Each above mentioned system is based on its own cryptosystem that allows secure communication, and users don’t have to worry about anything. One of the most reliable cryptosystems is RSA cryptosystem which is described in the following thesis. Number theory behind the RSA cryptosystem discuses the areas of prime numbers, divisibility and congruences, and it’s presented in the introduction of the thesis. Other mathematical concepts follow which are closely related to the RSA: primality tests, generation of large prime numbers, factorization and discrete logarithms. In conclusion we present some of the more famous attacks on the RSA cryptosystem, under which we see when is the RSA most vulnerable and what are its weaknesses.