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We consider permutations avoiding a pattern of length three under the family of Mallows distributions. In particular, for any pattern , we obtain rather precise results on the asymptotic probability as n → ∞ that a permutation under the Mallows distribution with parameter q ∈ (0, 1) avoids the pattern. By a duality between the parameters q and , we...
Random signal generation and processing
![Figure 2. The convergence of E[X 3 n ]/ √ n to its limiting value from...](publication/369063571/figure/fig1/AS:11431281125258461@1678248800652/The-convergence-of-EX-3-n-n-to-its-limiting-value-from-Eq-411_Q320.jpg)
![Figure 4. The exact values of c m for which log E[X m n ] ∼ c m √ n for...](publication/369063571/figure/fig2/AS:11431281125258462@1678248800683/The-exact-values-of-c-m-for-which-log-EX-m-n-c-m-n-for-small-m_Q320.jpg)
Let $\{U(n)\}_{n \geq 0}$ be a sequence of independent random variables such that $U(n)$ is distributed uniformly on $\{0, 1, 2 \dots n\}$. The Ulam-Kac adder is the history-dependent random sequence defined by $X_{n + 1} = X_{n} + X_{U(n)}$ with the initial condition $X_0 = 1$. We show that for each $m \geq 1$, it holds that $\log E[X_n^m]/\sqrt{n...
Citations
... A combination of chaos and LFSR was proposed by R. K. Koppanati et alwith a focus on efficient computational algorithm meant for resource-limited devices [11].W. Mao et al. proposed a hardware RNG in tandem with a LFSR based scrambler to generate a robust secure key. This unique combination is meant to reduce bias to zero by offsetting the noise sources to generate a very low bias bitstream [15].S. T. Allawihave developed a LFSR based diffusion scheme for colour images. This is done on a row-by-row basis followed by a column-by-column basis [1]. ...
In more recent times data continues to be generated at a very unprecedented scale. This is a result of the pervasive nature of modern-day digitisation. As such, it is absolutely critical that this data only be accessed by the trusted parties concerned in an effort to maintain the privacy of individuals. One particular type data that could severely compromise the identity and privacy of an individual is ‘medical data’. With a focus on medical images, this work proposes a novel ‘fractalized’ chaos-cellular automata encryption scheme, implemented on Cyclone IV EP2C35F672C6 FPGA, resulting in a hardware-based concurrent security solution. The scheme entails three stages of diffusion, which arise from different mechanisms. In tandem with the diffusion process is the “On the Fly” process of confusion governed by a Linear feedback Shift Register (LFSR), all of which in implemented by applying the nature of fractals. The security architecture occupies 16,351 Logic Elements (LEs) with 230 registers on the target FPGA with the power dissipation of 133.39 mW. Further, the encryption achieves near zero correlation with the average entropy of 15.17156 that ensures the statistical properties. In addition, the security framework requires 12.13 ms to encrypt a 256 × 256 × 16 DICOM image which results in the throughput of 86.44 Mbps. The proposed encryption resists the brute force attack and chosen plain text attack by achieving a very large span of keyspace.
... To increase the security of LSB steganography, we use the concept of LFSR (a random number generator) [4] in steganography. Linear feedback shift register (LFSR) is a shift register where the input bit is a linear function of the previous state. ...
... It can be used as a seed generator. In [8], an improved true random number generator (TRNG) is proposed, which comprises a low-bias hardware random number generator (HRNG) and a scrambler based on LFSR. The HRNG reduces both DC offset from the noise sources and offset voltage from the comparator to generate low-bias bit stream. ...
This paper introduces a random number generator (RNG) based on the avalanche noise of two diodes. A true random number generator (TRNG) generates true random numbers with the use of the electronic noise produced by two avalanche diodes. The amplified outputs of the diodes are sampled and digitized. The difference between the two concurrently sampled and digitized outputs is calculated and used to select a seed and to drive a pseudo-random number generator (PRNG). The PRNG is an xorshift generator that generates 1024 bits in each cycle. Every sequence of 1024 bits is moderately modified and output. The TRNG delivers the next seed and the next cycle begins. The statistical behavior of the generator is analyzed and presented.
