On the correlation and sensitivity of so far statistical randomness tests based on runs

Abstract—Random numbers play a very important role in cryptography. More precisely, almost cryptographic primitives are ensured their security based on random values such as random key, nonces, salts... Therefore, the assessment of randomness according to statistical tests is really essential for measuring the security of cryptographic algorithms. In this paper, we focus on so far randomness tests based on runs in the literature. First, we have proved in detail that the expected number of gaps (or blocks) of length in a random sequence of length is . Secondly, we have evaluated correlation of some tests based on runs so far using Pearson coefficient method [5, 6] and Fail-Fail ratio one [7, 8]. Surprisingly, the Pearson coefficient method do not show any strong linear correlation of these runs-based tests but the Fail-Fail ratio do. Then, we have considered the sensitivity of these runs tests with some basic transformations. Finally, we have proposed some new runs tests based on the sensitivity results and applied evaluations to some random sources. Tóm tắt—Số ngẫu nhiên đóng một vai trò quan trọng trong mật mã. Cụ thể, độ an toàn của hầu hết các nguyên thủy mật mã đều được đảm bảo dựa trên các giá trị ngẫu nhiên như khóa, nonce, salt… Do đó, việc đánh giá tính ngẫu nhiên dựa trên các kiểm tra thống kê là thực sự cần thiết để đo độ an toàn cho các thuật toán mật mã. Trong bài báo này, chúng tôi tập trung vào các kiểm tra ngẫu nhiên dựa vào run trong các tài liệu. Đầu tiên, chúng tôi chứng minh chi tiết rằng kỳ vọng số các gap (khối) độ dài trong một chuỗi ngẫu nhiên độ dài là . Sau đó, chúng tôi đánh giá mối tương quan của một số kiểm tra dựa vào run bằng phương pháp hệ số Pearson [5, 6] và tỷ số Fail-Fail [7, 8]. Đáng ngạc nhiên là phương pháp hệ số Pearson không cho thấy bất kỳ mối tương quan tuyến tính mạnh nào của các kiểm tra dựa vào run, trong khi đó tỷ số Fail-Fail lại chỉ ra. Tiếp theo, chúng tôi xem xét độ nhạy của các kiểm tra run này với một số phép biến đổi cơ bản. Cuối cùng, chúng tôi đề xuất một số kiểm tra run mới dựa trên các kết quả độ nhạy và đánh giá áp dụng chúng cho một số nguồn ngẫu nhiên.

RANDOM NUMBER GENERATOR TO SIMULATE CALL FLOW

The paper presents an approach to the development of generators providing the generation of sequences of random numbers for generating the flow of applications and determining the duration of connections.

Itamaracá: A Novel Simple Way to Generate Pseudo-random Numbers

In this paper was presented Itamaracá, a novel simple way to generate pseudo random numbers. In general vision we can say that Itamaracá tends to pass in some statistical tests like frequency, chi square, autocorrelation, run sequence and run test. As an effect to comparison also was taking into account the results of the function R and Between by Microsoft Excel and true random numbers by Random Org analyzed its distinctive characteristics as well as with the proposal model. In this sense, the goal of this study is contributing to growing the existing Pseudo Random Number Generators (PRNGs) portfolio.

Itamaracá: A Novel Simple Way to Generate Pseudo-random Numbers

In this paper was presented Itamaracá, a novel simple way to generate pseudo random numbers. In general vision we can say that Itamaracá tends to pass in some statistical tests like frequency, chi square, autocorrelation, run sequence and run test. As an effect to comparison also was taking into account the results of the function R and Between by Microsoft Excel and true random numbers by Random Org analyzed its distinctive characteristics as well as with the proposal model. In this sense, the goal of this study is contributing to growing the existing Pseudo Random Number Generators (PRNGs) portfolio.

Design of a Cryptographically Secure Pseudo Random Number Generator with Grammatical Evolution

This work investigates the potential of evolving an initial seed with Grammatical Evolution (GE), for the construction of cryptographically secure (CS) pseudo-random number generator (PRNG). We harness the flexibility of GE as an entropy source for returning initial seeds. The initial seeds returned by GE demonstrate an average entropy value of 7.920261600000001 which is extremely close to the ideal value of 8. The initial seed combined with our proposed approach, control_flow_incrementor, is used to construct both, GE-PRNG and GE-CSPRNG.The random numbers generated with CSPRNG meet the prescribed National Institute of Standards and Technology (NIST) SP800-22 requirements. Monte Carlo simulations established the efficacy of the PRNG. The experimental setup was designed to estimate the value for pi, in which 100,000,000 random numbers were generated by our system and which resulted in returning the value of pi to 3.146564000, with a precision up to six decimal digits. The random numbers by GE-PRNG were compared against those generated by Python’s rand() function for sampling. The sampling results, when measured for accuracy against twenty-nine real world regression datasets, showed that GE-PRNG had less error when compared to Python’s rand() against the ground truths in seventeen of those, while there was no discernible difference in the remaining twelve.

Generalized Galois-Fibonacci Matrix Generators Pseudo-Random Sequences

The article discusses various options for constructing binary generators of pseudo-random numbers (PRN) based on the so-called generalized Galois and Fibonacci matrices. The terms "Galois matrix" and "Fibonacci matrix" are borrowed from the theory of cryptography, in which the linear feedback shift registers (LFSR) generators of the PRN according to the Galois and Fibonacci schemes are widely used. The matrix generators generate identical PRN sequences as the LFSR generators. The transition from classical to generalized matrix PRN generators (PRNG) is accompanied by expanding the variety of generators, leading to a significant increase in their cryptographic resistance. This effect is achieved both due to the rise in the number of elements forming matrices and because generalized matrices are synthesized based on primitive generating polynomials and polynomials that are not necessarily primitive. Classical LFSR generators of PRN (and their matrix equivalents) have a significant drawback: they are susceptible to Berlekamp-Messi (BM) attacks. Generalized matrix PRNG is free from BM attack. The last property is a consequence of such a feature of the BM algorithm. This algorithm for cracking classical LFSR generators of PRN solves the problem of calculating the only unknown – a primitive polynomial generating the generator. For variants of generalized matrix PRNG, it becomes necessary to determine two unknown parameters: both an irreducible polynomial and a forming element that produces a generalized matrix. This problem turns out to be unsolvable for the BM algorithm since it is designed to calculate only one unknown parameter. The research results are generalized for solving PRNG problems over a Galois field of odd characteristics.

A Fast Markovian Method For Modeling Channel Noise In Neurons

Channel noise results from rapid transitions of protein channels from closed to open state and is generally considered as the most dominant source of electrical noise causing membrane-potential fluctuations even in the absence of synaptic inputs. The simulation of a realistic channel noise remains a source of possible error. Although the Markovian method is considered as the golden standard for appropriate description of channel noise, its computation time increasing exponentially with numbers of channels, it is poorly suitable to simulate realistic features. We describe here a novel algorithm for simulating ion channel noise based on Markov chains (MC). Although this new algorithm refers to a Monte-Carlo process, it only needs few random numbers whatever the number of channels involved. Our fast MC (FMC) model does not exhibit the drawbacks due to approximations based on stochastic differential equations. In fact, we show here, that these drawbacks can be highlighted even for a high number of channels.