An analysis of key generation efficiency of RSA cryptosystem in distributed environments

Thesis (Master)--Izmir Institute of Technology, Computer Engineering, Izmir, 2005Includes bibliographical references (leaves: 68)Text in English Abstract: Turkish and Englishix, 74 leavesAs the size of the communication through networks and especially through Internet grew, there became a huge need for securing these connections. The symmetric and asymmetric cryptosystems formed a good complementary approach for providing this security. While the asymmetric cryptosystems were a perfect solution for the distribution of the keys used by the communicating parties, they were very slow for the actual encryption and decryption of the data flowing between them. Therefore, the symmetric cryptosystems perfectly filled this space and were used for the encryption and decryption process once the session keys had been exchanged securely. Parallelism is a hot research topic area in many different fields and being used to deal with problems whose solutions take a considerable amount of time. Cryptography is no exception and, computer scientists have discovered that parallelism could certainly be used for making the algorithms for asymmetric cryptosystems go faster and the experimental results have shown a good promise so far. This thesis is based on the parallelization of a famous public-key algorithm, namely RSA

RSA Cryptosystem: An Analysis And Python Simulator

This project involves an exploration of the RSA cryptosystem and the mathematical concepts embedded within it. The first goal is to explain what the cryptosystem consists of, and why it works. Additional goals include detailing some techniques for primality testing, discussing integer factorization, modular exponentiation, and digital signatures, and explaining the importance of these topics to the security and efficiency of the RSA cryptosystem. The final goal is to implement all of these components into a full simulation of the entire RSA cryptosystem using the Python programming language

The Key to Cryptography: The RSA Algorithm

Cryptography is the study of codes, as well as the art of writing and solving them. It has been a growing area of study for the past 40 years. Now that most information is sent and received through the internet, people need ways to protect what they send. Some of the most commonly used cryptosystems today include a public key. Some public keys are based around using two large, random prime numbers combined together to help encrypt messages. The purpose of this project was to test the strength of the RSA cryptosystem public key. This public key is created by taking the product of two large prime numbers. We needed to find a way to factor this number and see how long it would take to factor it. So we coded several factoring algorithms to test this. The algorithms that were implemented to factor are Trial Division, Pollard’s Rho, and the Quadratic Sieve. Using these algorithms we were able to find the threshold for decrypting large prime numbers used in Cryptography

Fast Digital Convolutions using Bit-Shifts

An exact, one-to-one transform is presented that not only allows digital circular convolutions, but is free from multiplications and quantisation errors for transform lengths of arbitrary powers of two. The transform is analogous to the Discrete Fourier Transform, with the canonical harmonics replaced by a set of cyclic integers computed using only bit-shifts and additions modulo a prime number. The prime number may be selected to occupy contemporary word sizes or to be very large for cryptographic or data hiding applications. The transform is an extension of the Rader Transforms via Carmichael's Theorem. These properties allow for exact convolutions that are impervious to numerical overflow and to utilise Fast Fourier Transform algorithms.Comment: 4 pages, 2 figures, submitted to IEEE Signal Processing Letter

A Solution for Privacy-Preserving and Security in Cloud for Document Oriented Data (By Using NoSQL Database)

Cloud computing delivers massively scalable computing resources as a service with Internet based technologies those can share resources within the cloud users. The cloud offers various types of services that majorly include infrastructure as services, platform as a service, and software as a service and security as a services and deployment model as well. The foremost issues in cloud data security include data security and user privacy, data protection, data availability, data location, and secure transmission. In now day, preserving-privacy of data and user, and manipulating query from big-data is the most challenging problem in the cloud. So many researches were conducted on privacy preserving techniques for sharing data and access control; secure searching on encrypted data and verification of data integrity. This work  included preserving-privacy of document oriented data security, user privacy in the three phases those are data security at rest, at process and at transit by using Full Homomorphic encryption and decryption scheme to achieve afore most mentioned goal. This work implemented on document oriented data only by using NoSQL database and  the encryption/decryption algorithm such as RSA and Paillier’s cryptosystem in Java package with MongoDB, Apache Tomcat Server 9.1, Python, Amazon Web Service mLab for MongoDB as remote server.  Keywords: Privacy-Preserving, NoSQL, MongoDB, Cloud computing, Homomorphic encryption/decryption, public key, private key, RSA Algorithm, Paillier’s cryptosystem DOI: 10.7176/CEIS/11-3-02 Publication date:May 31st 202

On the Cyclotomic Quantum Algebra of Time Perception

I develop the idea that time perception is the quantum counterpart to time measurement. Phase-locking and prime number theory were proposed as the unifying concepts for understanding the optimal synchronization of clocks and their 1/f frequency noise. Time perception is shown to depend on the thermodynamics of a quantum algebra of number and phase operators already proposed for quantum computational tasks, and to evolve according to a Hamiltonian mimicking Fechner's law. The mathematics is Bost and Connes quantum model for prime numbers. The picture that emerges is a unique perception state above a critical temperature and plenty of them allowed below, which are parametrized by the symmetry group for the primitive roots of unity. Squeezing of phase fluctuations close to the phase transition temperature may play a role in memory encoding and conscious activity

Progress on probabilistic encryption schemes

The purpose of this master\u27s project is to study different probabilistic cryptography schemes. The older probabilistic schemes, Goldwasser-Micali and Blum-Goldwasser, will only be covered briefly for a historical perspective. Several new and promising schemes have appeared in the last 7 years, generating interest. I will be examining the Paillier and Damgard-Jurik schemes in depth. This report explains the mathematics behind the schemes along with their inherent benefits, while also suggesting some potential uses. Details are given on how I optimized the algorithms, with special emphasis on using the Chinese Remainder Theorem (CRT) in the Damgard-Jurik algorithm as well as the other algorithms. One of the main benefits these schemes posses is the additively homomorphic property. I explain the homomorphic properties in the description of the schemes and give an overview of these properties in Appendix A. I create software based in the Java Cryptography Extension (JCE) that is used to do a comparative study. This includes a simple message passing program for encrypted text. I create my own implementations of Paillier, Damgard-Jurik, and a variation of Paillier\u27s scheme as a Provider using the JCE. These implementations use the CRT along with other methods to increase performance and create optimized algorithms. The implementations are plugged into the message passing program with an implementation of RSA from another Provider. A comparative study of the timings of these three schemes is done to show which one performs better in different circumstances. Conclusions are drawn based on the results of the tests and my final opinions are stated