Pseudo-random number generator based on linear congruence and delayed Fibonacci method

Pseudo-random number generation techniques are an essential tool to correctly test machine learning processes. The methodologies are many, but also the possibilities to combine them in a new way are plenty. Thus, there is a chance to create mechanisms potentially useful in new and better generators. In this paper, we present a new pseudo-random number generator based on a hybrid of two existing generators - a linear congruential method and a delayed Fibonacci technique. We demonstrate the implementation of the generator by checking its correctness and properties using chi-square, Kolmogorov and TestU01.1.2.3 tests and we apply the Monte Carlo Cross Validation method in classification context to test the performance of the generator in practice.

Method for fast classification of MNIST digits on Arduino UNO board using LogNNet and linear congruential generator

The paper presents a method for forming a reservoir of a neural network LogNNet using a linear congruent pseudo-random number generator. This method made it possible to reduce the MNIST handwritten digit recognition time on the low-memory Arduino Uno board to 0.28 s for the LogNNet 784:20:10 configurations, with a classification accuracy of ~ 82%. It was found that the computations with integers gives an increase in the speed of the algorithm by more than 2 times in comparison with the algorithm using the real type when generating a chaotic time series. The developed method can be used to accelerate the calculations of edge devices in the field of “Internet of Things”, for example, for mobile medical devices, autonomous vehicle control systems and bionic suit control.

LXM: better splittable pseudorandom number generators (and almost as fast)

In 2014, Steele, Lea, and Flood presented SplitMix, an object-oriented pseudorandom number generator (prng) that is quite fast (9 64-bit arithmetic/logical operations per 64 bits generated) and also splittable . A conventional prng object provides a generate method that returns one pseudorandom value and updates the state of the prng; a splittable prng object also has a second operation, split , that replaces the original prng object with two (seemingly) independent prng objects, by creating and returning a new such object and updating the state of the original object. Splittable prng objects make it easy to organize the use of pseudorandom numbers in multithreaded programs structured using fork-join parallelism. This overall strategy still appears to be sound, but the specific arithmetic calculation used for generate in the SplitMix algorithm has some detectable weaknesses, and the period of any one generator is limited to 2 64 . Here we present the LXM family of prng algorithms. The idea is an old one: combine the outputs of two independent prng algorithms, then (optionally) feed the result to a mixing function. An LXM algorithm uses a linear congruential subgenerator and an F 2 -linear subgenerator; the examples studied in this paper use a linear congruential generator (LCG) of period 2 16 , 2 32 , 2 64 , or 2 128 with one of the multipliers recommended by L’Ecuyer or by Steele and Vigna, and an F 2 -linear xor-based generator (XBG) of the xoshiro family or xoroshiro family as described by Blackman and Vigna. For mixing functions we study the MurmurHash3 finalizer function; variants by David Stafford, Doug Lea, and degski; and the null (identity) mixing function. Like SplitMix, LXM provides both a generate operation and a split operation. Also like SplitMix, LXM requires no locking or other synchronization (other than the usual memory fence after instance initialization), and is suitable for use with simd instruction sets because it has no branches or loops. We analyze the period and equidistribution properties of LXM generators, and present the results of thorough testing of specific members of this family, using the TestU01 and PractRand test suites, not only on single instances of the algorithm but also for collections of instances, used in parallel, ranging in size from 2 to 2 24 . Single instances of LXM that include a strong mixing function appear to have no major weaknesses, and LXM is significantly more robust than SplitMix against accidental correlation in a multithreaded setting. We believe that LXM, like SplitMix, is suitable for “everyday” scientific and machine-learning applications (but not cryptographic applications), especially when concurrent threads or distributed processes are involved.

Attacking the linear congruential generator on elliptic curves via lattice techniques

In this paper we study the linear congruential generator on elliptic curves from the cryptographic point of view. We show that if sufficiently many of the most significant bits of the composer and of three consecutive values of the sequence are given, then one can recover the seed and the composer (even in the case where the elliptic curve is private). The results are based on lattice reduction techniques and improve some recent approaches of the same security problem. We also estimate limits of some heuristic approaches, which still remain much weaker than those known for nonlinear congruential generators. Several examples are tested using implementations of ours algorithms.

Compressed Sensing System for a Fingerprint Image Recognition Using Sensing Matrix with Chaotic Model-Based Deterministic Row Indexes

This paper proposes a novel design approach for a secured compressed sensing system for fingerprint sensing and transmission. In the proposed design, the first stage is acquiring the signal followed by sparsely modeling it using Orthogonal Matching Pursuit (OMP) algorithm then compressing. In addition to compressing, we multiply the sparse modeled data by a novel, deterministic, and partially orthogonal Discrete Cosine Transform (DCT) sensing matrix to guarantee its security. Furthermore, the construction of the sensing matrix uses a modified Multiplicative Linear Congruential Generator (MLCG) to select the row index appropriately from chaotically re-arranged rows of DCT pseudo-randomly. On the other hand, the compressed image's simultaneous recovery and decryption accomplished using a convex optimization method—the proposed system tested by employing different image and security assessment techniques. The results show that we have archived a better Peak Signal to Noise Ratio (PSNR) than the recommended value for wireless transmission using samples below 25%.

Compressed Sensing System for a Fingerprint Image Recognition Using Sensing Matrix with Chaotic Model-Based Deterministic Row Indexes

This paper proposes a novel design approach for a secured compressed sensing system for fingerprint imaging and its transmission. In the proposed design, the first stage is acquiring the signal followed by sparsely modeling it using Orthogonal Matching Pursuit (OMP) algorithm. In addition to compressing, to guaranty its security, we multiply the sparse modeled data by a novel deterministic partially orthogonal Discrete Cosine Transform (DCT) sensing matrix. Furthermore, the construction of the sensing matrix uses a modified Multiplicative Linear Congruential Generator (MLCG) to select the row index appropriately from chaotically re-arranged rows of DCT pseudo-randomly. On the other hand, the simultaneous recovering and decryption of the compressed image accomplished with the help of a convex optimization method. The proposed system tested by employing different image and security assessment techniques. The results show that we have archived better Peak Signal to Noise Ratio (PSNR) than the recommended value for wireless transmission using samples below 25%.

Co-simulation of linear congruential generator by using Xilinx system generator and MATLAB Simulink

<p>Arbitrary numerals are utilized in a wide range of uses. Genuine arbitrary numeral generators are moderate and costly for some applications while pseudo arbitrary numeral generators (RNG) do the trick for most applications. This paper fundamentally concentrates around the co-simulation of the linear congruential generator (LCG) model utilizing the Xilinx System generator and checking on Matlab Simulink. The design is obtained from the LCG calculation offered by Lehmer. Word lengths decrease strategy has been utilized to streamline the circuit. Simulation has been done effectively. The effective N bit LCG is structured and tried by utilizing demonstrating in MatLab Simulink. The Co-simulation of the model is done by utilizing the Xilinx system generator. This paper conducts an exhaustive search for the best arbitrary numeral generator in a full period linear congruential generator (LCG) with the largest prime numbers.</p>