Cryptographically Secure Pseudorandom Number Generator Research Articles

A forensic framework to improve digital image evidence administration in IIoT✰

The extensive growth of Industrial Internet of Things (IIoT) has prompted cyber attackers to commence a variety of attacks which need to be identified to maintain the security of industrial data and services. Digital forensics is an extravagant need to detect cyber attacks and to identify cybercriminals. While conducting criminal investigation using digital forensics, there is high probability of leakage of collected digital evidence. Hence, the need for a secure and lightweight cryptosystem arises to protect it from cyber-attacks. In the present paper, authors aim to design a novel forensic framework for digital evidence administration using advanced encryption and preservation mechanisms. Authors focus to encrypt and preserve only digital image evidence but can be deployed on other types of multimedia data like video frames. Three types of Chaos-map algorithms namely 4D hyperchaotic map, 2D Arnold Cat map (ACM) and Henon Map have been utilized to encrypty and decrypt digital image evidence which enable high sensitivity and dependency on initial conditions, quasi-randomness, and ergodicity to digital content. The proposed approaches have been analyzed on different groups of images of different size and validated using various security parameters such as unified average changing intensity (UACI), correlation coefficient, and the number of pixels changing rate (NPCR). Image transformation and compression has been performed after encryption process using Fast Fourier Transformation (FFT). The proposed work has been analyzed using histogram and auto-correlation. Experimentations have provided the values of the correlation coefficient of plain images near 1 and the value of adjacent cipher images near zero which show a strong correlation. The evaluated results for UACI are more than 33 % for every considered images. The value for NPCR should be near 100 % and here the calculated results for each image are above 99 %. The complexity of the proposed encryption algorithm is O(n) due to key generation using a cryptographically secure pseudo-random number generator (CSPRNG). The compressed and transformed image evidence have been stored into decentralized blockchain to ensure the integrity and confidentiality. Decentralized blockchain has been used as a reliable and promising solution to preserve digital evidence due to its distinct features like secure peer to peer communication, improved trust and transparency among participants, integrity, confidentiality, immutability, without risk of single point-of-failure. The proposed digital forensic model is able to prevent various threats and security challenges which can contaminate or tamper off digital pieces of evidence and assures improved digital evidence administration and defensibility. In the proposed scheme, the encryption process takes only 2–3 s to perform the encryption of each size of image.

Cryptographically Secured Pseudo-Random Number Generators: Analysis and Testing with NIST Statistical Test Suite

There are several areas of knowledge in which (pseudo-)random numbers are necessary, for example, in statistical–mathematical simulation or in cryptography and system security, among others. Depending on the area of application, it will be necessary that the sequences used meet certain requirements. In general, randomness and uniformity conditions are required in the generated sequences, which are checked with statistical tests, and conditions on sequence unpredictability if the application is in security. In the present work, a literature review on cryptographically secure pseudo-random number generators (CSPRNGs) is carried out, they are implemented, and a critical analysis of their statistical quality and computational efficiency is performed. For this purpose, different programming languages will be used, and the sequences obtained will be checked by means of the NIST Statistical Test Suite (NIST STS). In addition, a user’s guide will be provided to allow the selection of one generator over another according to its statistical properties and computational implementation characteristics.

Enhancing Post-Quantum Cryptography: Exploring Mathematical Foundations and Comparative Analysis of Different Cryptographic Algorithm

Abstract: This research paper surveys the landscape of cryptography, encompassing historical origins and modern applications. Beginning with foundational concepts, it explores encryption, decryption, ciphers, and keys, spanning symmetric and asymmetric cryptography. Historical context unfolds, tracing cryptography from ancient Egyptian hieroglyphs to Julius Caesar's cipher. The study then transitions to contemporary subjects. Elliptic Curves and Cryptography are investigated, showcasing their significance in secure communication, demonstrating ECC key exchange and AES-GCM encryption using python and Comparative analysis of ECC, RSA, and Diffie-Hellman sheds light on their performance. Zero-Knowledge Proofs are introduced as tools for privacy-preserving verification followed by an exploration of various Zero-Knowledge Proof (ZKP) protocols. By presenting practical implementation examples using Python, the paper illustrates how these proofs can be applied in real-world scenarios. Random Number Generation is examined and distinction between pseudorandom number generators (PRNGs) and cryptographically secure PRNGs (CSPRNGs) is emphasized conducting a thorough comparative analysis of PRNGs and CSPRNGs, considering factors like correlation, independence, periodicity, and entropy. Furthermore, the section evaluates the performance of different random number generation techniques. Fully Homomorphic Encryption emerges as a groundbreaking concept, discussing its mathematical properties, practical implementation, parameter selection, and optimization techniques enabling computation on encrypted data. Cryptographic Secret Sharing Schemes are explored for secure information distribution. The paper concludes by delving into the Chinese Remainder Theorem's applications within modern cryptographic protocols, particularly in RSA decryption and the integration factorization process of the RSA public key cryptosystem. It also provides a comprehensive overview of the theoretical foundations of primality testing, a pivotal aspect of the RSA algorithm. Overall, this research paper provides a comprehensive exploration of cryptography's historical context, core concepts, advanced techniques, and practical implementations, offering valuable insights into the realm of secure communication

Quantum encryption in phase space with displacement operators

In photonic computing, the quantum systems consist of coherent states and squeezed coherent states. Common quantum gates found in these systems are: phase shift, displacement, and squeezing gates. These gates are all unitary and reversible. Outside of quantum systems, coherent states also plays a significant role in coherent optical communications with speeds of hundreds of gigabits per second. Secure optical communications is generally implemented at the data layer with classical symmetric encryption such as Advanced Standard Encryption or AES. This inevitably allows any wiretapping to capture the transmitted data either in the plaintext mode or in the encrypted ciphertext mode in the optical infrastructure. The recent and rapid developments in Quantum computing further lift up the need for quantum secure communications in the optical infrastructure. This paper proposes a novel quantum encryption in the coherent optical domain utilizing a displacement operator and implementing with IQ-MZM optical modules, called Quantum Encryption in Phase Space or QEPS. The communication peers share a secret used to seed cryptographic pseudo random number generators to produce a synchronized random number at both the transmitter and receiver. The synchronized random numbers are used to establish displacement operators to encrypt the coherent states at the transmission and decrypt the cipher coherent states at the receiver. Therefore, malicious parties tapping along the fibre line would not extract the message in transit from optical domain due to a high Bit Error Rate or BER. The optimal displacement operator is split into a standard 16-QAM and a random phase shift operator to enhance the transmission security. We analysis the transmission security with the wiretap channel model for semantic security. We have simulated the QEPS encryption and decryption for two data modulation schemes: QPSK and 16-QAM over 80 km for transmission speeds of 56 Gbps for QPSK and 112 Gbps for 16-QAM.

A tradeoff paradigm shift in cryptographically-secure pseudorandom number generation based on discrete logarithm

Discrete logarithmic pseudorandom number generators are a prevailing class of cryptographically-secure pseudorandom number generators (CSPRNGs). In generators of this type, the security parameter affects both security and performance. This adds to the design complexity via creating a critical tradeoff between security and performance. This research is an attempt at shifting the security-performance tradeoff paradigm in this realm. To this end, we propose a modification to Gennaro’s pseudorandom number generator via replacing word-wise arithmetic operations with bit-wise logical operations in trapdoor and hard-core functions. The security of our generator (like that of Gennaro’s) is based on the hardness of a special variant of the discrete logarithm problem. We establish an equivalence between the specific variant of the discrete logarithm problem with the standard problem. Moreover, we demonstrate that in the modified generator, performance will be almost independent of the security parameter as logical operations can be performed in register level without the interference of the Arithmetic-Logic Unit (ALU). This relaxes the security-performance tradeoff and allows designers to maneuver more flexibly in the tradeoff space. We implement and evaluate our proposed generator and prove its security. Our CSPRNG is deemed random by all randomness tests in NIST SP 800-22 suite.

LWE Based Quantum-Resistant Pseudo-Random Number Generator

In the realm of cryptography, computational statistics, gaming, simulation processes, gambling, and other related fields, the design of Cryptographically Secure Pseudo-Random Number Generators (CSPRNGs) poses a significant challenge. With the rapid advancement of quantum computing, the imminent "quantum-threat" looms closer, posing a risk to our current cryptographically secure PRNGs. Consequently, it becomes crucial to address these threats seriously and develop diverse tools and techniques to ensure that cryptographically secure Pseudo-Random Number Generators (PRNGs) remain unbreakable by both classical and quantum computers. this paper presents a novel approach to constructing an effective Quantum-Resistant Pseudo-Random Number Generator (QRPRNG) using the principles of lattice-based Learning with Errors (LWE). LWE is considered quantum-resistant due to its reliance on the hardness of problems like the Shortest Vector Problem and Closest Vector Problem. Our work focuses on developing a QRPRNG that utilizes a Linear Feedback Shift Register (LFSR) to generate a stream of pseudo-random bits. To construct a secure seed for the QRPRNG, LWE is employed. The proposed QRPRNG incorporates a secure seed input to the LFSR, and employs a Homomorphic function to protect the security of the finite states within the LFSR. NIST statistical tests are conducted to evaluate the randomness of the generated output by the constructed QRPRNG. The proposed QRPRNG achieves a throughput of 35.172 Mbit/s.

Efficiently Secure Data Communications Based on CBC-RC6 and the Overflow Field of Timestamp Option in an IPv4 Packet

In recent times, many researchers have directed their research efforts towards increasing the privacy and security requirements in the wireless communication networks area. The reason for this is the inappropriateness of using traditional security processes for reliable, efficient, and robust communication over networks that are not secured. Thus, this study contributes to the enhancement of security in wireless communication networks by proposing the use of steganography combined with cryptography so that secret information can be sent using IPv4 as cover to conceal secret messages, thereby, securing the messages. Steganography is described as the process of concealing secret data in a way that it cannot be traced by an intruder. Here, the intruder is unable to detect any modifications made to the original media. Meanwhile, cryptography is referred to as the process through which plain text can be converted into ciphertext to enable the transmission of data through certain channels of communication in a format that cannot be read by a normal user. Network Steganography is a mechanism that involves the use of protocols for communication that control the path of the channel via the network. Initially, the TCP/IP protocols have been a good candidate for network steganography, due to the many benefits that can be derived from its use. One of such benefits is that allows the creation of a variety of concealed channels that can be used for secret communication. In order to enable communication over the network, the use of Cryptographically Secure Pseudo-Random Number Generator (CSPRNG) is employed in the proposed system so that the encryption/decryption key can be generated. The initial step in our study involves encrypting the secret data that needs to be protected, and this is achieved through the use of the CBC-RC6 cryptographic algorithm. After the encryption has been successfully performed, a covert channel is created for the encrypted data through the use of the Overflow field of the Timestamp option of IPv4. With this method, debugging and measurement over networks is carried out using the timestamp option, and the aim of this is to build storage-based network steganography. One of the strategies used in this work to deter the possible detection of covert communication is the deployment of legal overflow data.

On Random Number Generation for Kernel Applications

An operating system kernel uses cryptographically secure pseudorandom number generator (CSPRNG) for creating address space layout randomization (ASLR) offsets to protect memory addresses of processes from exploitation, storing users’ passwords securely and creating cryptographic keys. However, at present, popular kernel CSPRNGs such as Yarrow, Fortuna and /dev/(u)random which are used by MacOS/iOS/FreeBSD, Windows and Linux/Android kernels respectively lack the very crucial property of non-reproducibility of their generated bitstreams which is used to nullify the scope of predicting the bitstream. This paper proposes a CSPRNG called Cryptographically Secure Pseudorandom Number Generator for Kernel Applications (KCS-PRNG) which generates non-reproducible bitstreams. The proposed KCS-PRNG presents an efficient design uniquely configured with two new non-standard and verified elliptic curves and clock-controlled Linear Feedback Shift Registers (LFSRs) and a novel method to consistently generate non-reproducible random bitstreams of arbitrary lengths. The generated bitstreams are statistically indistinguishable from true random bitstreams and provably secure, resilient to important attacks, exhibits backward and forward secrecy, exhibits exponential linear complexity, large period and huge key space.

Design and Test of an Integrated Random Number Generator with All-Digital Entropy Source.

In the cybersecurity field, the generation of random numbers is extremely important because they are employed in different applications such as the generation/derivation of cryptographic keys, nonces, and initialization vectors. The more unpredictable the random sequence, the higher its quality and the lower the probability of recovering the value of those random numbers for an adversary. Cryptographically Secure Pseudo-Random Number Generators (CSPRNGs) are random number generators (RNGs) with specific properties and whose output sequence has such a degree of randomness that it cannot be distinguished from an ideal random sequence. In this work, we designed an all-digital RNG, which includes a Deterministic Random Bit Generator (DRBG) that meets the security requirements for cryptographic applications as CSPRNG, plus an entropy source that showed high portability and a high level of entropy. The proposed design has been intensively tested against both NIST and BSI suites to assess its entropy and randomness, and it is ready to be integrated into the European Processor Initiative (EPI) chip.

Analisis Pola Identifikasi Zero Knowledge Proof Dengan Algoritma Feige Fiat Shamir Menggunakan Blum Blum Shub

Protocol Zero Knowledge Proof is one of the protocols in Cryptography that has a fairly good level of security, because it applies the concept of "Truly Zero Knowledge Proof" which is not leaking any information. This protocol is used in the Fiat Shamir, Guillou Quisquater and Schnorr Feige Algorithms, all of which are Cryptographic Algorithms using private keys and public keys. In the Public key, all three of these Algorithms use a random number generator at the values p and q to get the public key. In this study, the author will generate a public key generation test using CPRNG (Cryptographically-secure Pseudo-Random Number Generator) with the Blum Blum Shub algorithm. The test will be conducted on the Fiat Feige Algorithm, the formation of the key will use the Blum Blum Shub Algorithm, but the Identification Protocol still uses the Fiat Shamir Feige Algorithm. The results of this study show the Feige Fiat Algorithm with the Blum Blum Shub Algorithm as the key builder successfully identifies the pattern sent by the signer.

Beyond Statistical Analysis in Chaos-Based CSPRNG Design

The design of cryptographically secure pseudorandom number generator (CSPRNG) producing unpredictable pseudorandom sequences robustly and credibly has been a nontrivial task. Almost all the chaos-based CSPRNG design approaches invariably depend only on statistical analysis. Such schemes designed to be secure are being proven to be predictable and insecure day by day. This paper proposes a design and instantiation approach to chaos-based CSPRNG using proven generic constructions of modern cryptography. The proposed design approach with proper instantiation of such generic constructions eventually results in providing best of both worlds that is the provable security guarantees of modern cryptography and passing of necessary statistical tests as that of chaos-based schemes. Also, we introduce a new coupled map lattice based on logistic-sine map for the construction of CSPRNG. The proposed pseudorandom number generator is proven using rigorous security analysis as that of modern cryptography and tested using the standard statistical testing suites. It is observed that the generated sequences pass all stringent statistical tests such as NIST, Dieharder, ENT, and TestU01 randomness test suites.

Security Evaluation of Y00 Protocol Based on Time-Translational Symmetry Under Quantum Collective Known-Plaintext Attacks

In this paper, we concretely formulate to derive the attacker's success probability of obtaining the shared secret keys for the Y00 protocol under a combination of a quantum collective attack with infinitely-long known-plaintext, naming it “collective known-plaintext attack” in this work. In contrast, our previous work showed only the necessary condition to design Y00 transmitters to be information-theoretic secure. The keystone of the security evaluations in this work is the time-translational symmetry of the Y00 signals modulated by pseudo-random number generators, such as linear-feedback shift registers or Mersenne twisters. With the assist of a true-random deliberate-signal-randomization, information-theoretic security would be realized. By numerical simulations, we can determine whether the designed Y00 transmitters are information-theoretic secure. However, this work's security evaluation may not apply to the transmitters with cryptographically-secure pseudo-random number generators because they might not have time-translational symmetry, even though such Y00 transmitters may be securer. We also describe future challenges for theorists to accelerate designing securer Y00 transmitters.

Using bit flips as a source of randomness in cubeSat communication encryption

This paper will discuss the use of the randomness of bit flips in memory caused by ionized radiation in space, in conjunction with cryptographically-secure pseudorandom number generators (CSPRNGs) to improve upon CubeSat communication encryption. CubeSat encryption is largely unexplored but with their increasing popularity it is becoming vital that secure methods of CubeSat communication both among CubeSat constellations as well as to ground stations are established. While other methods of encryption exist and are widely used among CubeSats and larger satellites alike (AES, blowfish, CubeSat Space Protocol, etc.), the use of bit flip locations in memory are an untapped source of randomness to create more secure cryptographic systems. A bit flip simulator shall be designed and utilized in conjunction with the Command and Data Handling and Communications sub-systems of UBC Orbit, a student-lead satellite design team, to conduct research. The prototyped design will be tested at TRIUMF, a Canadian cyclotron research facility. The results and conclusions drawn from this study will provide a potential benefit to the detriment bit flips present to CubeSat communication by using them as a source of randomness for encryption.

Representations of Generalized Self-Shrunken Sequences

Output sequences of the cryptographic pseudo-random number generator, known as the generalized self-shrinking generator, are obtained self-decimating Pseudo-Noise (PN)-sequences with shifted versions of themselves. In this paper, we present three different representations of this family of sequences. Two of them, the p and G-representations, are based on the parameters p and G corresponding to shifts and binary vectors, respectively, used to compute the shifted versions of the original PN-sequence. In addition, such sequences can be also computed as the binary sum of diagonals of the Sierpinski’s triangle. This is called the B-representation. Characteristics and generalities of the three representations are analyzed in detail. Under such representations, we determine some properties of these cryptographic sequences. Furthermore, these sequences form a family that has a group structure with the bit-wise XOR operation.

Cryptographically Secure Pseudo-Random Number Generator IP-Core Based on SHA2 Algorithm.

In the context of growing the adoption of advanced sensors and systems for active vehicle safety and driver assistance, an increasingly important issue is the security of the information exchanged between the different sub-systems of the vehicle. Random number generation is crucial in modern encryption and security applications as it is a critical task from the point of view of the robustness of the security chain. Random numbers are in fact used to generate the encryption keys to be used for ciphers. Consequently, any weakness in the key generation process can potentially leak information that can be used to breach even the strongest cipher. This paper presents the architecture of a high performance Random Number Generator (RNG) IP-core, in particular a Cryptographically Secure Pseudo-Random Number Generator (CSPRNG) IP-core, a digital hardware accelerator for random numbers generation which can be employed for cryptographically secure applications. The specifications used to develop the proposed project were derived from dedicated literature and standards. Subsequently, specific architecture optimizations were studied to achieve better timing performance and very high throughput values. The IP-core has been validated thanks to the official NIST Statistical Test Suite, in order to evaluate the degree of randomness of the numbers generated in output. Finally the CSPRNG IP-core has been characterized on relevant Field Programmable Gate Array (FPGA) and ASIC standard-cell technologies.

Anti-Continuous Collisions User Based Unpredictable Iterative Password Salted Hash Encryption

Recently, providing services remotely over a network to enhance functionality and usability has become a trend. Applications regularly contain sensitive and personal information that should be managed and controlled by authorised persons. Thus, keeping the password security is important to prevent unauthorised users from impersonating other legal users. Hashing the password is one of the safety methods and means of preventing attacks. In this study, we proposed an iterative salted hash encryption mechanism named anti-continuous collision salted hash encryption (ACCSHE) that uses cryptographically secure pseudo random number generator (CSPRNG) and hashed with password data by secured hashing algorithm (SHA-256). The outcome manifests a flexibility of changing the results by controlling several key features, such as salt used, the range of the hashing process iterations or the minimum number of iterations without affecting the system's usability. The system efficiently prevented continues collision issue and effective processing time cost for an attacker.

Statistical Analysis, Ciphertext Only Attack, Improvement of Generic Quasigroup String Transformation and Dynamic String Transformation

Algebraic functions are the primitives that strengthen the cryptographic algorithms to ensure confidentiality of data and information. There is need for continues development of new and improvement of existing primitives. Quasigroup String transformation is one of those primitives that have many applications in cryptographic algorithms, Hash functions, and Pseudo-Random Number Generators. It is obvious that randomness and unpredictability is the requirement of every Cryptographic primitive. Most of those string transformations have not been implemented properly neither do they have security analysis. Cryptanalysis of existing scheme is as important as building new ones. In this paper, generic Quasigroup sting transformation is analyzed and found vulnerable to Ciphertext-Only-Attack. An adversary can compute the ciphertext to get the plaintext without prior knowledge of the plaintext. Pseudorandom numbers produced with generic string transformation can be reversed back to the original input with little effort. Therefore the generic quasigroup string transformation is compared with recently introduced string transformation and it is expected to provide better randomness and resistant to ciphertext-only-Attack. The proposed string transformation is suitable to one-way functions such as Hash functions, and pseudorandom number generators to mitigate the vulnerability of quasigroup string transformation to Ciphertext-Only-Attack. While the dynamic string transformation increase the difficulty level of predicting the substitution table used. The algorithms will be compared in terms of randomness using NIST statistical test suit, correlation Assessment and frequency Distribution.

FPGA implementation of SRAM PUFs based cryptographically secure pseudo-random number generator

The security of cryptographic protocols depends on the security of key sequences consisting of random numbers. In this paper, we design a Cryptographically Secure Pseudo-Random Number Generator (CSPRNG), which consists of a hash based Deterministic Random Bit Generator (DRBG) and a Get Entropy module. SRAM Physical Unclonable Functions (PUFs) are regarded as entropy sources, providing entropy data with enough entropy for CSPRNG. The construction of Get Entropy module is proposed to verify the availability of SRAM PUFs and compress the entropy data into truly random seeds that are fed into DRBG. This CSPRNG can reseed itself dynamically and can monitor the entropy of entropy sources in real time. The system is implemented and tested on Altera DE2. The test results show that, the pseudo-random numbers generated by this system can pass all random tests of National Institute of Standards and Technology (NIST) SP800-22 Test Suite and the throughput is up to 598.1 Mbps. Through the security discussion, this CSPRNG is theoretically confirmed that it can be securely applied to cryptographic protocols.

Anti-continuous collisions user-based unpredictable iterative password salted hash encryption

Recently, providing services remotely over a network to enhance functionality and usability has become a trend. Applications regularly contain sensitive and personal information that should be managed and controlled by authorised persons. Thus, keeping the password security is important to prevent unauthorised users from impersonating other legal users. Hashing the password is one of the safety methods and means of preventing attacks. In this study, we proposed an iterative salted hash encryption mechanism named anti-continuous collision salted hash encryption (ACCSHE) that uses cryptographically secure pseudo random number generator (CSPRNG) and hashed with password data by secured hashing algorithm (SHA-256). The outcome manifests a flexibility of changing the results by controlling several key features, such as salt used, the range of the hashing process iterations or the minimum number of iterations without affecting the system's usability. The system efficiently prevented continues collision issue and effective processing time cost for an attacker.

Interleaved Sequences of Geometric Sequences Binarized with Legendre Symbol of Two Types

A pseudorandom number generator is widely used in cryptography. A cryptographic pseudorandom number generator is required to generate pseudorandom numbers which have good statistical properties as well as unpredictability. An m-sequence is a linear feedback shift register sequence with maximal period over a finite field. M-sequences have good statistical properties, however we must nonlinearize m-sequences for cryptographic purposes. A geometric sequence is a binary sequence given by applying a nonlinear feedforward function to an m-sequence. Nogami, Tada and Uehara proposed a geometric sequence whose nonlinear feedforward function is given by the Legendre symbol. They showed the geometric sequences have good properties for the period, periodic autocorrelation and linear complexity. However, the geometric sequences do not have the balance property. In this paper, we introduce geometric sequences of two types and show some properties of interleaved sequences of the geometric sequences of two types. These interleaved sequences have the balance property and double the period of the geometric sequences by the interleaved structure. Moreover, we show correlation properties and linear complexity of the interleaved sequences. A key of our observation is that the second type geometric sequence is the complement of the left shift of the first type geometric sequence by half-period positions.