RSA Cryptosystem Research Articles

Meeting the Security Requirements of Electronic Medical Records in the ERA of High-Speed Computing

This study has two objectives. First, it aims to develop a system with a highly secured approach to transmitting electronic medical records (EMRs), and second, it aims to identify entities that transmit private patient information without permission. The NTRU and the Advanced Encryption Standard (AES) cryptosystems are secured encryption methods. The AES is a tested technology that has already been utilized in several systems to secure sensitive data. The United States government has been using AES since June 2003 to protect sensitive and essential information. Meanwhile, NTRU protects sensitive data against attacks through the use of quantum computers, which can break the RSA cryptosystem and elliptic curve cryptography algorithms. A hybrid of AES and NTRU is developed in this work to improve EMR security. The proposed hybrid cryptography technique is implemented to secure the data transmission process of EMRs. The proposed security solution can provide protection for over 40years and is resistant to quantum computers. Moreover, the technique provides the necessary evidence required by law to identify disclosure or misuse of patient records. The proposed solution can effectively secure EMR transmission and protect patient rights. It also identifies the source responsible for disclosing confidential patient records. The proposed hybrid technique for securing data managed by institutional websites must be improved in the future.

An Enhanced and Secured RSA Key Generation Scheme (ESRKGS)

Public-key cryptography can be claimed as the greatest and an excellent revolution in the field of cryptography. A public-key cryptosystem is used for both confidentiality and authentication. One such public-key cryptosystem is the RSA cryptosystem. In this paper, a modified and an enhanced scheme based on RSA public-key cryptosystem is developed. The proposed algorithm makes use of four large prime numbers which increases the complexity of the system as compared to traditional RSA algorithm which is based on only two large prime numbers. In the proposed Enhanced and Secured RSA Key Generation Scheme (ESRKGS), the public component n is the product of two large prime numbers but the values of Encryption (E) and Decryption (D) keys are based on the product of four large prime numbers (N) making the system highly secured. With the existing factorization techniques, it is possible only to find the primes p and q. The knowledge of n alone is not sufficient to find E and D as they are based on N. The time required for cryptanalysis of ESRKGS is higher than traditional RSA cryptosystem. Thus the system is highly secure and not easily breakable. A comparison is done between the traditional RSA scheme, a recent RSA modified scheme and our scheme to show that the proposed technique is efficient.

A secure and efficient ECC‐based user anonymity preserving single sign‐on scheme for distributed computer networks

AbstractA user authentication in the distributed computer networks (DCNs) plays a crucial rule to verify whether the user is a legal user and can therefore be granted access to the requested services to that user. In recent years, several RSA‐based single sign‐on mechanisms have been proposed in DCNs. However, most of them cannot preserve the user anonymity when possible attacks occur. The user devices are usually battery limited (e.g., cellular phones) and the elliptic‐curve cryptosystem is much efficient than RSA cryptosystem for the battery‐limited devices. In this paper, we aim to propose a new secure elliptic‐curve cryptosystem‐based single sign‐on mechanism for user authentication and key establishment for the secure communications in a DCNs using biometric‐based smart card. In our scheme, a user only needs to remember a private password and his or her selected unique identity to authenticate and agree on a high‐entropy cryptographic one‐time session key with a provider to communicate over untrusted public networks. Through formal and informal security analysis, we show that our scheme prevents other known possible attacks. In addition, we perform simulation on our scheme for the formal security verification using the widely‐accepted Automated Validation of Internet Security Protocols and Applications tool. The simulation results ensure that our scheme is secure against replay and man‐in‐the‐middle attacks. Furthermore, our scheme provides high security along with lower computational cost and communication cost, and as a result, our scheme is much suitable for the battery‐limited devices as compared to other related RSA‐based schemes. Copyright © 2014 John Wiley & Sons, Ltd.

TIMING ATTACK ANALYSIS ON THE HARDWARE ENCRYPTOR SHIPKA

Nowadays hardware encryptors are often used for information security; despite the equipment are more expensive than analogous software. First of all; it depends on the high level of reliability; which hardware encryptors can provide. One example of hardware encryptors is the personal means of cryptographic information security SHIPKA. It has been substantiated that the personal means of cryptographic information security SHIPKA prone to timing attacks. Algorithms used in RSA cryptosystem; such as Simple Modular Exponentiation; Montgomery reduction; Chinese Remainder Theorem; have been considered. It has been reported how timing attacks can be performed. Blinding has been suggested to be used in SHIPKA as countermeasures to prevent timing attacks on RSA.

Cryptography: optional subject in the degree in computer engineering in information technologies

Cryptography subject is part of the curriculum of the Bachelor’s Degree in Computer Engineering in Information Systems, at the University of Salamanca. This subject becomes easy to understand if the history of Cryptography is used. The basic mathematics includes the following main topics: Modular arithmetic, algebraic curves, finite fields and number theory. Cryptography is a means of protecting personal information to avoid an eavesdropper can access it. From the first century AD with the Julius Caesar cipher to the present day with RSA, ElGamal, knapsack or elliptic curve cryptosystems, the Cryptography has evolved. In this paper we will show the syllabus of Cryptography subject and how the history knowledge supposes an important part of it, and helps students to acquire the skills and competences included in the subject curriculum.

Improved Shamir''s CRT-RSA Algorithm: Revisit with the Modulus Chaining Method

RSA signature algorithms using the Chinese remainder theorem (CRT-RSA) are approximately four-times faster than straightforward implementations of an RSA cryptosystem. However, the CRT-RSA is known to be vulnerable to fault attacks; even one execution of the algorithm is sufficient to reveal the secret keys. Over the past few years, several countermeasures against CRT-RSA fault attacks have tended to involve additional exponentiations or inversions, and in most cases, they are also vulnerable to new variants of fault attacks. In this paper, we review how Shamir's countermeasure can be broken by fault attacks and improve the countermeasure to prevent future fault attacks, with the added benefit of low additional costs. In our experiment, we use the side-channel analysis resistance framework system, a fault injection testing and verification system, which enables us to inject a fault into the right position, even to within 1 μs. We also explain how to find the exact timing of the target operation using an Atmega128 software board.

CARRY SAVE COMMON MULTIPLICAND MONTGOMERY FOR RSA CRYPTOSYSTEM

RSA public key cryptosystem provides encryption and digital signatures. With growth of key size an efficient design of RSA in terms of area, frequency, throughput and power consumption is hard to achieve. Also with the different type of attacks possible, a need for secure RSA cryptosystem which is attack resistant has arisen. This study presents RSA design with Montgomery powering ladder and proposed carry save common multiplicand Montgomery on FPGAs. Since the modular exponentiation is based on Montgomery powering ladder therefore it is power attack resistant. Common multiplicand Montgomery modular multiplication reduces the complexity by computing once the common operations in modular squaring and modular multiplication. The proposed carry save common multiplicand Montgomery modular multiplication maintains intermediate results in carry save form and utilizes the DSP slices to convert the redundant results into binary at the end of the modular multiplication. The proposed RSA design implemented on FPGAs is efficient in terms of area, frequency, power consumption and is power attack resistant.

FPGA Implementation of 16 bit RSA Cryptosystem for Text Message

The rapid growth of the internet and electronic commerce has brought to the forefront the issue of privacy in electronic communication. In order to protect the information from unauthorized parties we need to mask the information before sending it through a communication channel. Currently RSA is one of the algorithms which are not broken by hackers due to its mathematical complexity. This paper presents a design and implementation of 16-bit RSA Cryptosystem. The entire cryptosystem is divided in to three parts: key generation, encryption and decryption. The key generation is carried out by using random number generator LFSR, “Sieve of Eratosthenes” algorithm for prime number detection, Booth multiplier for multiplication and Extended Euclidean algorithm to find GCD of the public key and Euler‟s Totient Function. Encryption and decryption is carried out by Modular Multiplication and Modular Exponentiation by using LR binary method. The encryption and decryption of the text message “NAGARJUNA COLLEGE” is verified using proposed RSA algorithm. The design is simulated using Modelsim10.2b simulator and finally implemented on Sparten-6 FPGA using Xilinx 13.4 software. Area and timing parameters are computed with respect to Spartan-6 FPGA. The results obtained from simulation are validated using MATLAB code.

AN EFFICIENT METHOD FOR IMPROVING THE COMPUTATIONAL PERFORMANCE OF THE CUBIC LUCAS CRYPTOSYSTEM

AbstractThe cubic version of the Lucas cryptosystem is set up based on the cubic recurrence relation of the Lucas function by Said and Loxton [‘A cubic analogue of the RSA cryptosystem’, Bull. Aust. Math. Soc.68 (2003), 21–38]. To implement this type of cryptosystem in a limited environment, it is necessary to accelerate encryption and decryption procedures. Therefore, this paper concentrates on improving the computation time of encryption and decryption in cubic Lucas cryptosystems. The new algorithm is designed based on new properties of the cubic Lucas function and mathematical techniques. To illustrate the efficiency of our algorithm, an analysis was carried out with different size parameters and the performance of the proposed and previously existing algorithms was evaluated with experimental data and mathematical analysis.

H-RABIN CRYPTOSYSTEM

Cryptography is the science of using mathematics that's used to hide information or data that is being sent between participants in a way that prevents other people from reading it. The need of exchanging messages secretly promoted the creation of cryptosystems to enable receivers to interpret the exchanged information. In this study, a particular public key cryptosystem called Rabin Cryptosystem is presented considered with the help of Chinese Reminder Theorem. Since the decryption algorithm of the Rabin cryptosystem is based on computing square roots modulo n, where n = p.q where p and q are primes. This study suggests a modification of Rabin cryptosystem that can make the cryptosystem more immune against some attacks. This modification focuses on considering n = p. q. r where p, q and r are primes. This new modification of Rabin cryptosystem is called H-Rabin Cryptosystem. Also, some basic mathematical concepts are explained and it finally compares the H-Rabin Cryptosystem, RSA cryptosystem and Rabin cryptosystem in terms of security and efficiency. This H-Rabin cryptosystem is a public key cryptosystem where the private key is composed of three primes, p, q and r and a public key composed of n = p. q. r and it is based on the hardness of factoring. Therefore, this new modification can make the cryptosystem more immune against some future attacks.

Algebraic Analysis of Object-Based Key Assignment Schemes

The confidentiality of information is an important aspect of security. One way to achieve the confidentiality is through restricting access to information to the authorized users only. Access control can be enforced by using encryption. In this case, all the information is encrypted and keys are assigned to users such that each key reveals the authorized part of the information. Key assignment can be classified as key-based or object-based schemes based on the focus of the scheme. Sabri and Khedri [1] present algebraic structures to specify algebraically cryptosystems by capturing the common properties of ciphers, secrets and keys. Also, these structures are used for the analysis of security properties in object-based key assignment schemes. However, these structures are abstract, and no linkage has been proposed to the existing cryptosystems. In this paper, we extend their work by giving concrete models for their algebraic structures. We give concrete models to Vigenere, transposition ciphers, DES, and RSA cryptosystems. Also, we investigate the effects of extra algebraic properties that some cryptosystems may have on the security analysis of object-based schemes.

Efficient FPGA Implementation of RSA Coprocessor Using Scalable Modules

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 15.725MHz, 17.629MHz 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.

Digital Image Encryption Based on RSA Algorithm

Abstract: Information Security has become an important issue in data communication. Cryptography has come up as a solution, and plays an important role in information security systems. This paper presents an introduction to the science of cryptography and explains the RSA cryptosystem. It also presents the comparison between RSA cryptosystem with DES and Blowfish cryptosystems applied on greyscale image.

Modified Rabin Cryptosystem through Advanced Key Distribution System

In this paper, an asymmetric cryptosystem Rabin Cryptosystem has been modified by adding an advanced message authentication system with it. The proposed modified Rabin Cryptosystem is a combination of symmetric and asymmetric key cryptosystem that is hybrid cryptosystem. In the symmetric part, the sender and the receiver share a secret key between themselves which is added with the plaintext to change the plaintext. The shared secret key is fixed for a session between two users. It can be different for different sessions and different users. In the asymmetric part, the modified plaintext is encrypted using Rabin Cryptosystem. Two extra values will be sent along with the cipher text to the receiver. In the decryption process, Chinese Remainder Theorem will be applied along with the two extra values which were received with the cipher text to decipher it. Then the shared secret key between the sender and the receiver will have to be applied to get the original plaintext. Even if any intruder succeeds to decipher the cipher text, he would get the modified plaintext. As he I. Introduction Technology around us is growing very fast, and security has become the major issue in this fast growing technical world. Every moment a new threat is being produced to disrupt the security of both data and network, and to guard us against these security threats, many new security mechanisms are also being produced. Cryptography is one very ancient yet strong mechanism that saves our data from the hands of the attackers. In this paper, we have proposed a new cryptographic mechanism which is a fine combination of symmetric and asymmetric cryptosystem. Section 1 contains the detailed description of the algorithm proposed, along with the flowchart and example of encryption and decryption process. Section 2 contains some results of the encryption and decryption procedure of the Modified Rabin Cryptosystem. It also shows the performance analysis and comparisons of the Modified Rabin Cryptosystem with RSA and Rabin Cryptosystem using several parameters. Section 3 describes the contribution of this paper in the field of cryptography. In section 4 we have drawn the conclusion of this paper. Section 5 shows the acknowledgement, and in the last section we have listed the references.

Better Lattice Constructions for Solving Multivariate Linear Equations Modulo Unknown Divisors

At CaLC 2001, Howgrave-Graham proposed the polynomial time algorithm for solving univariate linear equations modulo an unknown divisor of a known composite integer, the so-called partially approximate common divisor problem. So far, two forms of multivariate generalizations of the problem have been considered in the context of cryptanalysis. The first is simultaneous modular univariate linear equations, whose polynomial time algorithm was proposed at ANTS 2012 by Cohn and Heninger. The second is modular multivariate linear equations, whose polynomial time algorithm was proposed at Asiacrypt 2008 by Herrmann and May. Both algorithms cover Howgrave-Graham’s algorithm for univariate cases. On the other hand, both multivariate problems also become identical to Howgrave-Graham’s problem in the asymptotic cases of root bounds. However, former algorithms do not cover Howgrave-Graham’s algorithm in such cases. In this paper, we introduce the strategy for natural algorithm constructions that take into account the sizes of the root bounds. We work out the selection of polynomials in constructing lattices. Our algorithms are superior to all known attacks that solve the multivariate equations and can generalize to the case of arbitrary number of variables. Our algorithms achieve better cryptanalytic bounds for some applications that relate to RSA cryptosystems.

A Tiny RSA Cryptosystem based on Arduino Microcontroller Useful for Small Scale Networks

RSA Cryptography is a well-known example of public key cryptographic algorithms that involves robust encryption/decryption processes. In this paper, a microcontroller based RSA is designed and proposed. Arduino Mega2560R3 microcontroller supported with external memory and a screen touch LCD as well as a double keypad has been used under the programming of C language to implement the proposed RSA coprocessor with 32 bits. It was found that the trade of between message size and the encryption time can be drawn as a liner relationship according to the block size of the encryption phase. However, such design with a MCU provided with a small solar cell (and off course with a backup battery) as well as small block sizes is considered useful for the use in wireless sensor network (WSN) applications due to the ease of connecting the MCU to the WSN which as well avoid the processing time of encryption/decryption processes that could be executed by the MCU instead of the life limited sensors.

Notions for RSA integers

The key-generation algorithm for the RSA cryptosystem is specified in several standards, such as PKCS#1, IEEE 1363-2000, FIPS 186-3, ANSI X9.44, or ISO/IEC 18033-2. All of them substantially differ in their requirements. This indicates that for computing a 'secure' RSA modulus it does not matter how exactly one generates RSA integers. In this work, we show that this is indeed the case to a large extent. First, we give a theoretical framework that enables us to easily compute the entropy of the output distribution of the considered standards and show that it is comparatively high. To do so, we compute for each standard the number of integers they define up to an error of very small order and discuss different methods of generating integers of a specific form. Second, we show that factoring such integers is hard, provided factoring a product of two primes of similar size is hard.

Security of Multivariate Signature Scheme Using Non-commutative Rings

Multivariate Public Key Cryptosystems (MPKC) are candidates for post-quantum cryptography. Rainbow is a digital signature scheme in MPKC, whose signature generation and verification are relatively efficient. However, the security of MPKC depends on the difficulty in solving a system of multivariate polynomials, and the key length of MPKC becomes substantially large compared with that of RSA cryptosystems for the same level of security. The size of the secret and public keys in MPKC has been reduced in previous research. The NC-Rainbow is a signature scheme in MPKC, which was proposed in order to reduce the size of secret key of Rainbow. So far, several attacks against NC-Rainbow have been proposed. In this paper, we summarize attacks against NC-Rainbow, containing attacks against the original Rainbow, and analyze the total security of NC-Rainbow. Based on the cryptanalysis, we estimate the security parameter of NC-Rainbow at the several security level.

Improving the computational efficiency of modular operations for embedded systems

Abstract Security protocols such as IPSec, SSL and VPNs used in many communication systems employ various cryptographic algorithms in order to protect the data from malicious attacks. Thanks to public-key cryptography, a public channel which is exposed to security risks can be used for secure communication in such protocols without needing to agree on a shared key at the beginning of the communication. Public-key cryptosystems such as RSA, Rabin and ElGamal cryptosystems are used for various security services such as key exchange and key distribution between communicating nodes and many authentication protocols. Such public-key cryptosystems usually depend on modular arithmetic operations including modular multiplication and exponentiation. These mathematical operations are computationally intensive and fundamental arithmetic operations which are intensively used in many fields including cryptography, number theory, finite field arithmetic, and so on. This paper is devoted to the analysis of modular arithmetic operations and the improvement of the computation of modular multiplication and exponentiation from hardware design perspective based on FPGA. Two of the well-known algorithms namely Montgomery modular multiplication and Karatsuba algorithms are exploited together within our high-speed pipelined hardware architecture. Our proposed design presents an efficient solution for a range of applications where area and performance are both important. The proposed coprocessor offers scalability which means that it supports different security levels with a cost of performance. We also build a system-on-chip design using Xilinx’s latest Zynq-7000 family extensible processing platform to show how our proposed design improve the processing time of modular arithmetic operations for embedded systems.

페르마정리에 기반하는 오류 주입 공격에 안전한 classical RSA 암호시스템

스마트카드, 전자여권 등과 같은 내장형 장치(embedded system) 환경이 늘어나고, 민감한 데이터의 보안에 대한 수요가 증가함에 따라 다양한 부채널 공격에 대한 암호시스템의 안전한 구현이 중요시 되고 있다. 특히, 오류 주입공격은 암호 시스템 구현에 큰 위협 중 하나이며, 하나의 평문-암호문 쌍에 의해 전체 시스템의 안전성이 위협을 받을수 있기 때문에 암호시스템 구현자에 의해 심각하게 고려되어야 한다. 오류 주입 공격을 방지하는 몇몇 기술은 다양한 암호시스템을 위해 도입되었지만 여전히 classical RSA 암호시스템에 적용되는 실질적인 오류 주입 공격 대응책으로는 부족하다. 본 논문은 classical RSA 암호시스템을 위한 효율적인 오류 주입 공격 대응법을 제안한다. 제안하는 대응방법은 페르마의 정리를 사용하며 추가 연산이 적다는 이점이 있다. Esmbedded devices such as smart cards and electronic passports highly demand security of sensitive data. So, the secure implementation of the cryptographic system against various side-channel attacks are becoming more important. In particular, the fault injection attack is one of the threats to the cryptosystem and can destroy the whole system only with single pair of the plain and cipher texts. Therefore, the implementors must consider seriously the attack. Several techniques for preventing fault injection attacks were introduced to a variety of the cryptosystem, But the countermeasures are still inefficient to be applied to the classical RSA cryptosystem. This paper introduces an efficient countermeasure against the fault injection attack for the classical RSA cryptosystem, which is based on the famous Fermat's theorem. The proposed countermeasure has the advantage that it has less computational overhead, compared with the previous countermeasures.