Blum-Blum-Shub Research Articles

A New Cryptographic Key Planning Algorithm Based on Blum Blum Shub

The Blum Blum Shub (BBS) algorithm is one of the known powerful pseudo random number generators. This algorithm can be used for key generation. BBS is basically based on the product of two large prime numbers and a seed value. The selection of these values is a critical issue. In this study, a new approach is proposed to overcome this problem. In the proposed approach, a prime number pool is first created. At this point, the user sets a start and end value. The primes in this range are generated and stored in an array. Then, two primes are randomly selected from this prime number pool with chaotic maps. The positions of these prime numbers in the array are recorded. The seed value is taken as the sum of the positions of these two primes. In other words, the parameters to be selected will be randomly selected in the ranges that the user will enter at that moment. In this study, two random bit sequences were obtained in this way. These sequences are 1 million bits long. NIST SP 800-22 tests were applied to these sequences and the sequences successfully completed all tests.

Performance Analysis Of The Combination Of Blum Blum Shub And Rc5 Algorithm In Message Security

This research aims to enhance message security in the RC5 algorithm by integrating it with the Blum Blum Shub (BBS) algorithm. The rapid growth in data and information exchange, driven by advancements in information and communication technology, demands robust security against attacks such as eavesdropping, interruption, and data modification. Cryptography, particularly with symmetric and asymmetric keys, becomes a solution to maintain message confidentiality. The RC (Rivest Cipher) algorithm, specifically RC5, has become a popular choice in network applications due to its speed and variable key length complexity. This study attempts to improve the quality of encryption keys by integrating the Blum Blum Shub (BBS) method, a mathematical random number generator algorithm. RC5 and BBS are used together to secure messages, producing ciphertext that is difficult to predict and smaller in file size compared to the standard RC5 method. The test results show that the processing speed is independent of the number of characters in the plaintext, while the encrypted file size resulting from the RC5-BBS combination is more efficient than using the default RC5. In conclusion, integrating BBS into RC5 can enhance the security and efficiency of the encryption algorithm, with the potential for widespread application in cryptography-based data security

Adopsi Generator Kunci Euler Number dan Pembangkit Kunci Blum Blum Shub untuk Meningkatkan Confidentiality Level pada Extended Vigenere

The Vigenere algorithm is an encryption model that is still being developed in the field of information security today. One aspect that is considered important in the field of information security is confidentiality. The problem of achieving high message or information thresholds is very important in the field of information security. Extended Vigenere is known as an evolution of Vigenere that implements more character sets. One of Vigenere's development algorithms is to modify the key generator used. This experiment aims to test the effect of information confidentiality on the use of the Blum Blum Shub (BBS) key generator and the Euler number applied to Extended Vigenere. The BBS key generation method and Euler number are used sequentially. As a sample, short astronomical observation conversations sent via telegram with a file size of 1 KB were used. Experiments were carried out using different key lengths, namely 32-bit keys and 64-bit keys. As a measurement metric, the entropy calculation of the Extended Vigenere output is used. The results obtained are a significant increase in information confidentiality with an entropy achievement value of more than 79% of the optimum entropy

IMPLEMENTASI ALGORITMA BLUM BLUM SHUB PADA KUIS SANDI SEMAPHORE BERBASIS AUGMENTED REALITY

Semaphore is a way to send and receive news by using a flag, paddle, trunk, bare hands or gloves. The semaphore learning at School at this time still uses the Scout's manual and it is only in the form of 2D images and it is also delivered by the Scout coach. So that students tend to get bored in learning the semaphore movement and lack of understanding and education in the learning process in this modern era. From the existing problems, the semaphore movement learning application and semaphore quiz were built using augmented reality technology based on android to provide interesting and interactive learning. This application was built by adding the Blum-Blum Shub (BBS) algorithm for the randomization process which functions to generate random numbers in a mathematical process with the resulting output is a series of binary numbers. Application created uses Unity 3D, and developed uses the RUP (Rational Unifed Process) method. With this application, it can make easier for students to understand the material in semaphore learning

Pembangkitan Kunci Beaufort Cipher Dengan Teknik Blum-blum Shub pada Pengamanan Citra Digital

Data security is not only due to the complexity of the algorithms used, but one of the most important factors is the security of the keys used. One of the most popular data that needs to be backed up today is digital images. However, these days, the algorithms used to back up data are often attacked. This is because the structure of the key formations used is still weak. One of the data security algorithms that form a simple key is the Beaufort cipher. It relies on the duplication of key characters to form the key for each protected element. Key generators based on blum-blum shub technology can generate very random and difficult-to-guess keys, so the strength of the keys you use can enhance the resilience of protected data. Keys generated based on blum-blum shub technology will later be used in the process of encrypting and decrypting pixel values in digital images.

Generate Beaufort Cipher Key Based on Blum-Blum Shub For Secure Digital Image

Data security is not only due to the complexity of the algorithms used, but one of the most important factors is the security of the keys used. One of the most popular data that needs to be backed up today is digital images. However, these days, the algorithms used to back up data are often attacked. This is because the structure of the key formations used is still weak. One of the data security algorithms that form a simple key is the Beaufort cipher. It relies on the duplication of key characters to form the key for each protected element. Key generators based on blum-blum shub technology can generate very random and difficult-to-guess keys, so the strength of the keys you use can enhance the resilience of protected data. Keys generated based on blum-blum shub technology will later be used in the process of encrypting and decrypting pixel values ​​in digital images.

Secure CT-Image Encryption for COVID-19 Infections Using HBBS-Based Multiple Key-Streams.

The task of preserving patient data is becoming more sophisticated with the evolution of technology and its integration with the medical sector in the form of telemedicine and electronic health (e-health). Secured medical image transmission requires adequate techniques for protecting patient privacy. This study aims at encrypting Coronavirus (COVID-19) images of Computed Tomography (CT) chest scan into cipherimages for secure real-world data transmission of infected patients. Provably safe pseudo-random generators are used for the production of a "key-stream" to achieve high privacy of patient data. The Blum Blum Shub (BBS) generator is a powerful generator of pseudo-random bit-strings. In this article, a hashing version of BBS, namely Hash-BBS (HBBS) generator, is presented to exploit the benefits of a hash function to reinforce the integrity of extracted binary sequences for creating multiple key-streams. The NIST-test-suite has been used to analyze and verify the statistical properties of resulted key bit-strings of all tested operations. The obtained bit-strings showed good randomness properties; consequently, uniform distributed binary sequence was achieved over the key length. Based on the obtained key-streams, an encryption scheme of four COVID-19 CT-images is proposed and designed to attain a high grade of confidentiality and integrity in transmission of medical data. In addition, a comprehensive performance analysis was done using different evaluation metrics. The evaluation results of this study demonstrated that the proposed key-stream generator outperforms the other security methods of previous studies. Therefore, it can be successfully applied to satisfy security requirements of transmitting CT-images for COVID-19 patients.

User Authentication Secure by Randomly Cubic Spline Curve and Blum Blum Shub Algorithm

With the tremendous development witnessed by the world in recent times, computer security significance expanded as insurance procedure of registering systems and authentication the user with scientific and technological developments are increasing every day. This assurance procedure is connected for touchy information such of electronic business, electronic learning, and electronic saving money exchange, online networking and more administrations over the web by utilizing login application to distinguish the character for doing this authentication. The problem by using some application login how to detected the user authentic and experimental data collection and separated the duplicated name that may be Confusion the system with speed detected and difficult attack. This paper solve this problem by used Cubic spline to easy represented name and easy detected by distance Euclidean equation, authentication techniques utilized as insurance process by securing name mix with Blum Blum Shub (BBS) algorithm that have randomly number. In this work, the application is founded on type name that the combine with (BBS) and represented by cubic spline, to detected user. The result of proposed work require randomly number to drawing the curve to detect and how much the different shape in cubic spline curve that can be detected. Assurance gives affirmation distinguished suitable security and all the more effortlessly least complex that developing popular in the online application that shows in result some portion of the paper

Design of a Novel Pseudo Random Generator based on Walsh Hadamard Transform and Bi S-Boxes

A cryptographic technique plays a decisive role in day-to-day life. Usually cryptographic algorithms yield confidentiality and authentication. Several cryptographic applications use random numbers and pseudo random numbers. In this paper, we propose a cryptographically secure pseudo random bit generator (CSPRBG) employing Walsh-Hadamard Transform (WHT) and S-boxes (G S-box and Algebraic S-box). CSPRBG is a major category in pseudo random bit generator (PRBG) and used Blum BlumShub (BBS) Generator for an initial condition. WHT is used in a vast variety of scientific and engineering applications, including bent functions and cryptanalytic optimization techniques in cryptography. S-box is the most crucial source to produce confusion and diffusion in the data and it is based on the algebraic structure of multiplicative cyclic group of the Galois field. The robustness of both the S-boxes inspected in terms of nonlinearity, strict avalanche criterion, bit independence criterion, linear and differential approximation probabilities. The target is to generate a lengthy unpredictable keystream with better performance. The random sequence generated by proposed generator passes the test of National Institute of Standards and Technology (NIST) suite. Meticulous analysishas been performed, in precise, statistical randomness test and random sequences generated from proposed generator can be used for many cryptographic applications specifically as inputs to stream cipher.

Hybrid Approach for PRNGs using BBS and Dithering Technique

Objectives: The cryptographically secure pseudo-random number generator Blum Blum-Shub (BBS) is a simple algorithm with a strong security proof, all of number generators that produced by BBS will be converted to (0, 1) using simplest form called Parity (even parity bit and odd parity bit).This approach proposed new method for extending bit space acquired from BBS based on dither matrix instead of (Parity) feature with saving of strength and security of crypto-key. Methods/Statistical Analysis: We used dithering techniques (2*2, 4*44) that provide continuous image of higher colors on a display of less color depth, for improving numbers that generated by BBS. And used some of statistical tests for measuring crypto-key strength such (run, poker, serial and frequency tests).The proposal algorithm has been programmed using c#.net 2013 Findings: This approach provides high extended on number space that generated from BBS by using Dithering techniques (2*2, 4*4), with saving of crypto-key randomness and guarantee passing of statistical tests, dithering techniques (8*8) is unsuitable for this purpose. Although, it provides height extension but decrease the randomness of key numbers. Application/Improvements: This approach proposed to replace (Parity) property with dithering techniques. It’s replaces max of gray level in dithering such (256) in 8 bit image with value of n , (p*q) in BBS , this may convert the domain of any number sets to dithering domain to be suitable for purpose. Keywords: Blum-Blum-Shub, Cryptography, Cryptography Key, Dithering, Pseudo Random Number generation (PRNGs)

A Hybrid Polybius-Playfair Music Cipher

Music has a versatile dimensionality; it can be used to express feelings, emotions and can also be used as a communicable language. Music and its attributes have been used in cryptography and steganography from a long time. Musical symbols and notes are used as replacement/substitution cipher. Using music as a cipher or cover media not only enhances the security of the message but also reduces its chance to be detected as an encoded or ciphered message. This paper proposes a hybrid Polybius and Playfair cipher which encodes the message into sequence of musical notes. The Playfair key matrix is generated using the Blum-Blum Shub generator. The bigrams of plain text message is first encrypted using Playfair cipher then individual character of the encrypted message is re-encrypted using Polybius cipher. The Playfair cipher enhances the security of the encrypted message over the simple substitution technique. The Polybius cipher then reduces the character set by appropriate number of symbols (here musical notes) for replacement. The basic 5X5 structure of key matrix in Polybius and Playfair is extended to 10X10 to hold the 95 prinTable characters of ASCII character set.

Blum BlumShub Pseudorandom Sequence based Peak Power Control in MC-CDMA System

This paperanalyses thePeak to Average Power Ratio (PAPR) for various sequences such as Walsh Hadamard (WH), Gold Sequence,Welch-Gong(WG)sequence and Blum BlumShub (BBS) sequence in Multicarrier Code Division Multiple Access(MC-CDMA)system. Inmultiuser MC-CDMA system, the Blum BlumShub(BBS) sequence provides reduced peak to mean envelope power ratio(PMEPR)when comparedto WH sequence. So,this BBS sequence can be considered as a good alternative for Walsh Hadamard (WH) sequence in reducing PAPR in MC-CDMA system.

A Practical Image Encryption Algorithm

Image encryption is the premises of secret image transmission in network.The paper discusses the characteristics of chaotic sequence and BlumBlumShub generator,and generates position scrambling matrix and coefficient disturbing matrix.Then two matrixes was used to encrypt image DWT coefficient,and experimental results show that the algorithm is fairly good in efficiency and practicality.

Fast BBS-sequence generation using Montgomery multiplication

VLSI modules are proposed for fast, efficient generation of high-throughput Blum–Blum-Shub (BBS) and BBS-like sequences using Montgomery multiplication, where postprocessing associated with Montgomery's algorithm can be eliminated.