Random number generation

Summary

Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outcome sequence will contain some patterns detectable in hindsight but unpredictable to foresight. True random number generators can be hardware random-number generators (HRNGs), wherein each generation is a function of the current value of a physical environment's attribute that is constantly changing in a manner that is practically impossible to model. This would be in contrast to so-called "random number generations" done by pseudorandom number generators (PRNGs), which generate numbers that only look random but are in fact pre-determined—these generations can be reproduced simply by knowing the state of the PRNG. Various applications of randomness have led to the development of different methods for generating random data. Some of these have

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https://en.wikipedia.org/wiki/Random_number_generation

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In computing, a hardware random number generator (HRNG), true random number generator (TRNG) or non-deterministic random bit generator (NRBG) is a device that generates random numbers from a physica

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A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of

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Statistical Analysis of Chao’s Immune System Simulation

Eric Winnington

Modeling the immune system (IS) means putting together a set of assumptions about its components (cells and organs) and their interactions. Simulations of a model show joint behavior of the components, which for complex realistic models is often impossible to find analytically. Simulations allow us to experiment on how initial concentrations and properties of the immune cells and viruses impact the IS behavior, and gain better quantitative and qualitative insight into how the IS works and why different behavior patterns occur. A simulation, once it has been created, must be reviewed both statistically and analytically as well as validated from the biological point of view. We analyzed Chao’s immune system simulation [1][2] from a statistical and analytical point. We explicited both the Markov chain which was simulated and the underlying process on which Chao’s stage-structured approach was built. Furthermore, we established a test protocol for timestep validation which Chao’s simulator passed. We evaluated Chao’s simulator’s dependence on the random number generator, which was shown to be negligible. Finally, we evaluated the simulator output and our major result is the discovery of a secondary response to a primary infection, an occurrence is not shown in Chao’s dissertation. A tertiary response to the infection is never possible due to the size of the secondary response caused by memory cells.

2005

Post-quantum cryptography is a branch of cryptography which deals with cryptographic algorithms whose hardness assumptions are not based on problems known to be solvable by a quantum computer, such as the RSA problem, factoring or discrete logarithms.This thesis treats two such algorithms and provides theoretical and practical attacks against them.The first protocol is the generalised Legendre pseudorandom function - a random bit generator computed as the Legendre symbol of the evaluation of a secret polynomial at an element of a finite field. We introduce a new point of view on the protocol by analysing the action of the group of Möbius transformations on the set of secret keys (secret polynomials).We provide a key extraction attack by creating a table which is cubic in the number of the function queries, an improvement over the previous algorithms which only provided a quadratic yield. Furthermore we provide an ever stronger attack for a new set of particularly weak keys.The second protocol that we cover is SIKE - supersingular isogeny key encapsulation.In 2017 the American National Institute of Standards and Technology (NIST) opened a call for standardisation of post-quantum cryptographic algorithms. One of the candidates, currently listed as an alternative key encapsulation candidate in the third round of the standardisation process, is SIKE.We provide three practical side-channel attacks on the 32-bit ARM Cortex-M4 implementation of SIKE.The first attack targets the elliptic curve scalar multiplication, implemented as a three-point ladder in SIKE. The lack of coordinate randomisation is observed, and used to attack the ladder by means of a differential power analysis algorithm.This allows us to extract the full secret key of the target party with only one power trace.The second attack assumes coordinate randomisation is implemented and provides a zero-value attack - the target party is forced to compute the field element zero, which cannot be protected by randomisation. In particular we target both the three-point ladder and isogeny computation in two separate attacks by providing maliciously generated public keys made of elliptic curve points of irregular order.We show that an order-checking countermeasure is effective, but comes at a price of 10% computational overhead. Furthermore we show how to modify the implementation so that it can be protected from all zero-value attacks, i.e., a zero-value is never computed during the execution of the algorithm.Finally, the last attack targets a point swapping procedure which is a subroutine of the three-point ladder. The attack successfully extracts the full secret key with only one power trace even if the implementation is protected with coordinate randomisation or order-checking. We provide an effective countermeasure --- an improved point swapping algorithm which protects the implementation from our attack.

EPFL2022

Multivariate extremes over a random number of observations

Simone Padoan, Stefano Rizzelli

The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated data, such as maxima of a random number of observations, are considered. We derive a limit theorem concerning the attractors for the distributions of the aggregated data, which boil down to a new family of max-stable distributions. We also connect the extremal dependence structure of classical max-stable distributions and that of our new family of max-stable distributions. Using an inversion method, we derive a semiparametric composite-estimator for the extremal dependence of the unobservable data, starting from a preliminary estimator of the extremal dependence of the aggregated data. Furthermore, we develop the large-sample theory of the composite-estimator and illustrate its finite-sample performance via a simulation study.

WILEY2020

EPFL2022