Random Bits Research Articles

Determining optimal parameters of algebraic fractals in zero-knowledge authentication protocols

Most information systems, especially on the Internet, have a distributed architecture with remote access and an insecure communication channel. In such systems, the tasks of permanent authorization mean implementing time intervals of user work without re-authentication are especially actual. The problem is that repeatedly sending a password increases the likelihood of it corruption. One solution is to use zero-knowledge protocols. In these protocols, passwords are not transmitted over the channel but are included in the algorithms as parameters. However, the computational complexity, as well as the finite number of passwords, limit their use, ensuring the relevance of further research. Focusing on object of the exchange protocols security, the use of algebraic fractal sets has been proposed as a potentially infinite source of data for passwords. In this work, algorithms were developed, implemented, and tested, which proved the higher reliability of fractal protocols in comparison with the reference generator of random bits (with an error probability of 0.5). It was also noted that the calculation operations have an insignificant influence on the overall time complexity of the exchange protocol as a whole. Practical recommendations for the use of fractals with a Hausdorff dimensionally of about 1.6 on the boundary of the Mandelbrot set are given. The paper also highlights the advantages of including color information in fractal sets, which gives about 3 times improving of confidential security indicators of communication protocol. The proposed algorithms do not require specialized software and can be implemented in the majority of network information systems as an additional module.

Time-delay signature elimination of chaotic laser via a self-feedback antisymmetric resonator.

A scheme for generating a chaotic output from a semiconductor laser while eliminating the time-delay signature (TDS) is proposed, leveraging the multi-path feedback provided by a self-feedback antisymmetric coupling fiber ring resonator (SACFRR). A theoretical model is developed to elucidate the feedback perturbation process in the proposed structure. The multi-path feedback can be modeled by incorporating the unit impulse response of the SACFRR into the modified Lang-Kobayashi-based model. We successfully eliminated the TDS using the SACFRR structure in our experimental demonstration. Further investigation into the impact of the coupling coefficient on the TDS revealed that the optimal value is 0.3, which results in the largest mapping area with the TDS below 0.03. The proposed structure is highly effective and simple to implement and integrate. As a result, the chaotic laser generated by this structure can serve as an efficient optical source for encrypted communications, chaotic Lidar, and random bit generation.

Parallel high-speed random bit generation based on wideband chaotic microcomb and wavelet high-pass filtering.

We propose and experimentally demonstrate a parallel ultra-fast random bit generation (RBG) scheme based on wideband chaotic microcomb, which utilizes a phase modulation and dispersive component broadening spectrum. The effective bandwidth of each comb tooth is increased by over 10-fold. Wavelet high-pass filtering (WHPF) is employed to make the probability density functions (PDFs) of the chaotic signal's amplitude unbiased, achieving high symmetry with a skewness coefficient |S| of 0.0026, and the RBG rate of a single channel reaches 200 Gbps. Furthermore, the autocorrelation properties of the random sequences from each comb tooth and the cross-correlation properties between different comb teeth are analyzed, confirming both true randomness and orthogonality. This scheme can simultaneously generate dozens of wideband chaotic combs in the wavelength range of 1500-1600 nm.

A novel superposition coding scheme based on polar code for multi‐user detection in underwater acoustic OFDM communication system

SummarySuperposition coding (SC) is a non‐orthogonal multiple access (NOMA) scheme for the downlink communication system, which allows signals of different users to be stacked and forwarded simultaneously in the same frequency band. The codeword for each user is assigned a different weight at the transmitter to avoid signal conflicts and interference after stacking, and successive interference cancellation (SIC) is adopted to decode. A novel SC scheme based on polar code, suitable for the downlink multi‐user underwater acoustic (UWA) communication system using orthogonal frequency division multiplexing (OFDM), is proposed in this paper. Polar code is utilized to create a nested code structure that is divided into several subsets. We exploit this feature of the polar codes and assign each subset to the corresponding user in the channel coding process. The information bits are placed on the independent subset for each user, and the random bits are placed on the subset of other users while all the users share the same set of frozen bits. Then, the codewords are stacked with different weights. The selection range of power factors can be expanded through the double superposition of the coding and the power domains, and higher system throughput and fairness can be achieved. The simulation and tank experiment results significantly verify the effectiveness of the proposed scheme, making it most suitable for the downlink UWA multi‐user communication systems.

Subsampling Suffices for Adaptive Data Analysis

Ensuring that analyses performed on a dataset are representative of the entire population is one of the central problems in statistics. Most classical techniques assume that the dataset is independent of the analyst’s query and break down in the common setting where a dataset is reused for multiple, adaptively chosen, queries. This problem of adaptive data analysis was formalized in the seminal works of Dwork et al. (STOC, 2015) and Hardt and Ullman (FOCS, 2014). We identify a remarkably simple set of assumptions under which the queries will continue to be representative even when chosen adaptively: The only requirements are that each query takes as input a random subsample and outputs few bits. This result shows that the noise inherent in subsampling is sufficient to guarantee that query responses generalize. The simplicity of this subsampling-based framework allows it to model a variety of real-world scenarios not covered by prior work. In addition to its simplicity, we demonstrate the utility of this framework by designing mechanisms for two foundational tasks, statistical queries and median finding. In particular, our mechanism for answering the broadly applicable class of statistical queries is both extremely simple and state of the art in many parameter regimes.

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.

Quantum-Secured Data Centre Interconnect in a field environment

In the evolving landscape of quantum technology, the increasing prominence of quantum computing poses a significant threat to the security of conventional public key infrastructure. Quantum key distribution (QKD), an established quantum technology at a high readiness level, emerges as a viable solution with commercial adoption potential. QKD facilitates the establishment of secure symmetric random bit strings between two geographically separated, trustworthy entities, safeguarding communications from potential eavesdropping. In particular, data centre interconnects can leverage the potential of QKD devices to ensure the secure transmission of critical and sensitive information in preserving the confidentiality, security, and integrity of their stored data. In this article, we present the successful implementation of a QKD field trial within a commercial data centre environment that utilises the existing fibre network infrastructure. The achieved average secret key rate of 2.392 kbps and an average quantum bit error rate of less than 2% demonstrate the commercial feasibility of QKD in real-world scenarios. As a use case study, we demonstrate the secure transfer of files between two data centres through the Quantum-Secured Virtual Private Network, utilising secret keys generated by the QKD devices. %This demonstration marks a significant milestone in the deployment of QKD across Singapore, establishing a foundation for widespread adoption and enhancing the infrastructure for practical, quantum-safe communication in commercial environments.

Shadow Simulation of Quantum Processes.

We introduce the task of shadow process simulation, where the goal is to simulate the estimation of the expectation values of arbitrary quantum observables at the output of a target physical process. When the sender and receiver share random bits or other no-signaling resources, we show that the performance of shadow process simulation exceeds that of conventional process simulation protocols in a variety of scenarios including communication, noise simulation, and data compression. Remarkably, we find that there exist scenarios where shadow simulation provides increased statistical accuracy without any increase in the number of required samples.

Communication Complexity of the Secret Key Agreement in Algorithmic Information Theory

It is known that the mutual information, in the sense of Kolmogorov complexity, of any pair of strings x and y is equal to the length of the longest shared secret key that two parties can establish via a probabilistic protocol with interaction on a public channel, assuming that the parties hold as their inputs x and y , respectively. We determine the worst-case communication complexity of this problem for the setting where the parties can use private sources of random bits. We show that for some x , y the communication complexity of the secret key agreement does not decrease even if the parties have to agree on a secret key, the size of which is much smaller than the mutual information between x and y . However, we discuss a natural class of x , y such that the communication complexity of the protocol declines gradually with the size of the derived secret key. The proof of the main result uses the spectral properties of appropriate graphs and the expander mixing lemma, as well as information-theoretic techniques, including constraint information inequalities and Muchnik’s conditional descriptions. A preliminary version of this article was published in the proceedings of MFCS 2020. In the present version, we give full proofs of all theorems and get rid of the assumption that the number of random bits used in the communication protocols is polynomial.

Combined Threshold Implementation

Physical security is an important aspect of devices for which an adversary can manipulate the physical execution environment. Recently, more and more attention has been directed towards a security model that combines the capabilities of passive and active physical attacks, i.e., an adversary that performs fault-injection and side-channel analysis at the same time. Implementing countermeasures against such a powerful adversary is not only costly but also requires the skillful combination of masking and redundancy to counteract all reciprocal effects.In this work, we propose a new methodology to generate combined-secure circuits. We show how to transform Threshold Implementation (TI)-like constructions to resist any adversary with the capability to tamper with internal gates and probe internal wires. For the resulting protection scheme, we can prove the combined security in a well-established theoretical security model.Since the transformation preserves the advantages of TI-like structures, the resulting circuits prove to be more efficient in the number of required bits of randomness (up to 100%), the latency in clock cycles (up to 40%), and even the area for pipelined designs (up to 40%) than the state of the art for an adversary restricted to manipulating a single gate and probing a single wire.

True random number generation based on temporal fluctuations of abalone shell coherent random lasers.

The output modes of random lasers exhibit randomness, making them a potential high-quality physical entropy source for generating random numbers. In this paper, we controlled a low-cost and easily fabricated abalone shell random laser, generating forward and backward coherent random lasers simultaneously in a single channel, resulting in highly diverse mode variations. After post-processing steps such as third-order difference calculations and exclusive-or (XOR) logic operations, we generated a random number sequence for the first time, to the best of our knowledge, based on the temporal fluctuations of biomimetic random laser coherent modes. The instantaneous generation rate reached a preliminary 40 Gbps. Moreover, the random bits satisfy requirements such as random distribution, independence, and absence of bias, successfully passing the NIST SP800-22 standard test, confirming the high quality of the random number sequence.

A Novel Chaotic System with Hyperbolic Tangent Terms and Its Application to Random Bit Generator and Image Encryption

A Novel Chaotic System with Hyperbolic Tangent Terms and Its Application to Random Bit Generator and Image Encryption

Intermittent microwave bursts of a semiconductor laser with an ultra-long loop for generating timing-based random bits.

Chaotic dynamics of semiconductor lasers under optical feedback are useful for random bit generation (RBG). By exploring on an ultra-long feedback loop, a single-mode laser in a route-to-chaos unveils an emission intensity with intermittent microwave bursts, for which a fast form of timing-based RBG is demonstrated. Each microwave burst corresponds to a packet of periodic intensity oscillations at the relaxation resonance. Numerous bursts are found intermittently within a round trip. Repetitions of these intermittent microwave bursts are observed across consecutive round trips. Randomness is extracted from the timing of the bursts as far as the feedback is reinitialized. With a 5-km fiber for feedback to the laser, over 104 intermittent bursts of microwave at 7 GHz are obtained per round trip, where the irregular timing in the envelope leads to RBG at 9.6 Gbps. Such experimental results feature the form of timing-based RBG that is very fast by comparison, carried by the microwave, and stored in the feedback nonlinear dynamics.

Real-Time Massive Parallel Generation of Physical Random Bits Using Weak-Resonant-Cavity Fabry-Perot Laser Diodes

We experimentally demonstrate a scheme for generating massively parallel and real-time physical random bits (PRBs) by using weak-resonant-cavity Fabry-Perot laser diodes (WRC-FPLDs) with optical feedback. By using external optical feedback to modify the nonlinear dynamic behavior of the longitudinal modes in WRC-FPLDs, the chaotic behavior of each channel can be induced under suitable feedback strength. By filtering these longitudinal modes, a real-time PRBs at 10 Gbits/s can be generated by using field programmable gate array (FPGA) board for the real-time post-processing of a single-channel chaotic signal. Considering the presence of up to 70 longitudinal modes within a broad spectral range exceeding 40 nm, each of these modes can be used to extract chaotic time sequences for random number generation. Therefore, our PRB generation scheme has the potential to achieve a data throughput of over 700 Gbits/s.

Analysing All-Optical Random Bit Sequences Using Gap-Based Approaches.

Quantum mechanical phenomena are revolutionizing classical engineering fields such as signal processing or cryptography. When randomness plays an important role, like in cryptography where random bit sequences guarantee certain levels of security, quantum mechanical phenomena allow new ways of generating random bit sequences. Such sequences have a lot of applications in the communication sector, e.g., regarding data transmission, simulation, sensors or radars, and beyond. They can be generated deterministically (e.g., by using polynomials, resulting in pseudo-random sequences) or in a non-deterministic way (e.g., by using physical noise sources like external devices or sensors, resulting in random sequences). Important characteristics of such binary sequences can be modelled by gap processes in conjunction with the probability theory. Recently, all-optical approaches have attracted a lot of research interest. In this work, an adaptation of the quantum key distribution setup is utilized for generating randomised bit sequences. The simulation results show that all-optically generated sequences very well resemble the theoretically ideal probability density characteristic. Additionally, an experimental optical setup is developed that confirms the simulation results. Furthermore, m-sequences show very promising results as well as Gold sequences. Additionally, the level of burstiness, i.e., the distribution of ones and zeros throughout the sequence, is studied for the different sequences. The results enable the finding that generator polynomials with concentrated non-zero coefficients lead to more bursty bit sequences.

Randomness Generation for Secure Hardware Masking – Unrolled Trivium to the Rescue

Masking is a prominent strategy to protect cryptographic implementations against side-channel analysis. Its popularity arises from the exponential security gains that can be achieved for (approximately) quadratic resource utilization. Many variants of the countermeasure tailored for different optimization goals have been proposed. The common denominator among all of them is the implicit demand for robust and high entropy randomness. Simply assuming that uniformly distributed random bits are available, without taking the cost of their generation into account, leads to a poor understanding of the efficiency vs. security tradeoff of masked implementations. This is especially relevant in case of hardware masking schemes which are known to consume large amounts of random bits per cycle due to parallelism. Currently, there seems to be no consensus on how to most efficiently derive many pseudo-random bits per clock cycle from an initial seed and with properties suitable for masked hardware implementations. In this work, we evaluate a number of building blocks for this purpose and find that hardware-oriented stream ciphers like Trivium and its reduced-security variant Bivium B outperform most competitors when implemented in an unrolled fashion. Unrolled implementations of these primitives enable the flexible generation of many bits per cycle, which is crucial for satisfying the large randomness demands of state-of-the-art masking schemes. According to our analysis, only Linear Feedback Shift Registers (LFSRs), when also unrolled, are capable of producing long non-repetitive sequences of random-looking bits at a higher rate per cycle for the same or lower cost as Trivium and Bivium B. Yet, these instances do not provide black-box security as they generate only linear outputs. We experimentally demonstrate that using multiple output bits from an LFSR in the same masked implementation can violate probing security and even lead to harmful randomness cancellations. Circumventing these problems, and enabling an independent analysis of randomness generation and masking, requires the use of cryptographically stronger primitives like stream ciphers. As a result of our studies, we provide an evidence-based estimate for the cost of securely generating n fresh random bits per cycle. Depending on the desired level of black-box security and operating frequency, this cost can be as low as 20 n to 30 n ASIC gate equivalents (GE) or 3 n to 4 n FPGA look-up tables (LUTs), where n is the number of random bits required. Our results demonstrate that the cost per bit is (sometimes significantly) lower than estimated in previous works, incentivizing parallelism whenever exploitable. This provides further motivation to potentially move low randomness usage from a primary to a secondary design goal in hardware masking research.

Efficient isochronous fixed-weight sampling with applications to NTRU

We present a solution to the open problem of designing a linear-time, unbiased and timing attack-resistant shuffling algorithm for fixed-weight sampling. Although it can be implemented without timing leakages of secret data in any architecture, we illustrate with ARMv7-M and ARMv8-A implementations; for the latter, we take advantage of architectural features such as NEON and conditional instructions, which are representative of features available on architectures targeting similar systems, such as Intel. Our proposed algorithm improves asymptotically upon the current approach based on constant-time sorting networks ( O ( n ) versus O ( n log 2 n ) ), and an implementation of the new algorithm applied to NTRU is also faster in practice, by a factor of up to 6.91 ( 591 % ) on ARMv8-A cores and 12.89 ( 1189 % ) on the Cortex-M4; it also requires fewer uniform random bits. This translates into performance improvements for NTRU encapsulation, compared to state-of-the-art implementations, of up to 50% on ARMv8-A cores and 72% on the Cortex-M4, and small improvements to key generation (up to 2.7% on ARMv8-A cores and 6.1% on the Cortex-M4), with negligible impact on code size and a slight improvement in RAM usage for the Cortex-M4.

High – Speed and Low Area-Efficient VLSI Architecture of Three-Operand Binary Adder

Three-operand binary adder is the basic functional unit to perform the modular arithmetic in various cryptography and Pseudo Random Bit Generator (PRBG) algorithms and also used in many applications. Carry Save Adder (CS3A) is the widely used technique to perform the three- operand addition. In carry save adder at final stage uses ripple carry adder which will cause large critical path delay. Moreover, a parallel prefix two-operand adder such as Han-Carlson Adder (HCA) can also be used for three-operand addition that significantly reduces the critical path delay with more area complexity. Hence, a new high-speed and area-efficient adder architecture is proposed using pre-compute bitwise addition followed by carry prefix computation logic to perform the three-operand binary addition that consumes substantially less area and less delay. The effectiveness of the proposed method is designed using Xilinx ISE 14.7

X-ray-driven multi-bit quantum random number generator

Random numbers are vital in cryptography, simulation modeling, and gambling. This study presents a scheme for a multi-bit quantum random number generator utilizing X-ray radiation. Using a homemade multi-pixel single-photon detector array, we extract randomness from three modes of X-ray radiation: arrival time, spatial position, and polarization direction. We employ the Toeplitz Matrix Hashing extractor for randomness distillation, resulting in the extraction of 40.4 million random bits at a rate of 33.7 bits per photon. The generated random numbers pass all test criteria in the National Institute of Standards and Technology statistical test suite. Our work paves what we believe to be a novel method for generating multi-bit quantum random numbers, promising enhanced security and reliability in various technological applications.

A Quantum Technology for Reinforcement Learning on Channel Assignment

AbstractProspective application of quantum technologies for reinforcement learning (RL) is an exciting surge in quantum fields. Quantum random number generators (QRNGs) produce high‐frequency random bits, with advantages of true randomness and device independence over pseudo‐random numbers. This work explores a new approach, called the quantum random numbers for multi‐armed bandit (QRN‐MAB) algorithm, for multi‐user access in wireless communication system upon random bits. The primary objective of the algorithm is to attain a stable assignment state without further exchange. QRN‐MAB utilizes random bits to learn channel features and conducts concurrent exchange to attain stability. This work finds that the intrinsic randomness property used in QRN‐MAB enables arrangement to maintain high accuracy and outperforms other classical algorithms. Additionally, the algorithm exhibits strong adaptability when the environment changes over time and quantum random numbers are advantageous over other pseudo‐random methods in achieving the target. This work provides an effective way for quantum technologies applications in RL and unfolds a promising avenue to stabilize assignment among multiple users.