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How elliptic curve cryptography works in TLS 1.3

Reading time 20 min
Views 20K
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A couple of reader alerts:

In order to (somewhat) simplify the description process and tighten the volume of the article we are going to write, it is essential to make a significant remark and state the primary constraint right away — everything we are going to tell you today on the practical side of the problematics is viable only in terms of TLS 1.3. Meaning that while your ECDSA certificate would still work in TLS 1.2 if you wish it worked, providing backwards compatibility, the description of the actual handshake process, cipher suits and client-server benchmarks covers TLS 1.3 only. Of course, this does not relate to the mathematical description of algorithms behind modern encryption systems.

This article was written by neither a mathematician nor an engineer — although those helped to find a way around scary math and reviewed this article. Many thanks to Qrator Labs employees.

(Elliptic Curve) Diffie-Hellman (Ephemeral)

The Diffie–Hellman legacy in the 21 century

Of course, this has started with neither Diffie nor Hellman. But to provide a correct timeline, we need to point out main dates and events.

There were several major personas in the development of modern cryptography. Most notably, Alan Turing and Claud Shannon both laid an incredible amount of work over the field of theory of computation and information theory as well as general cryptanalysis, and both Diffie and Hellman, are officially credited for coming up with the idea of public-key (or so-called asymmetric) cryptography (although it is known that in the UK there were made serious advances in cryptography that stayed under secrecy for a very long time), making those two gentlemen pioneers.

In what exactly?
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Total votes 21: ↑21 and ↓0 +21
Comments 0

A City Without Traffic Jams

Reading time 55 min
Views 4K

Chapter 2.
(the link to Chapter 1)

The Art of Designing Road Networks


Transport problems of a city through the eyes of a Computer Scientist


If I were recommended an article with the title “The Art of Designing Road Networks,” I would immediately ask how many road networks were built with the participation of its author. I must admit, my professional activity was far from road construction and was recently associated with the design of microprocessors where I, among other responsibilities, was engaged in the resource consumption of data switching. At that time my table stood just opposite the panoramic window which opened up a beautiful view of the long section of the Volgograd Highway and part of the Third Transport Ring with their endless traffic jams from morning to evening, from horizon to horizon. One day, I had a sudden shock of recognition: “The complexities of the data switching process that I struggle with on a chip may be similar to the difficulties the cars face as they flow through the labyrinth of road network”.
Probably, this view from the outside and the application of methods that were not traditional for the area in question gave me a chance to understand the cause of traffic jams and make recommendations on how to overcome the problem in practice.
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Total votes 13: ↑13 and ↓0 +13
Comments 2

Polygonal Mesh to B-Rep Solid Conversion: Algorithm Details and C++ Code Samples

Reading time 7 min
Views 4.7K
Boundary representation (B-rep) is the primary method of representing modeled objects in most geometric kernels, including our C3D Modeler kernel. The core algorithms that edit models, such as applying fillet operations, performing cutting operations, and obtaining flat projections require the precision of B-rep representations. The rapidly growing variety of 3D data in polygonal formats makes the task of model transformations from polygons into boundary representation increasingly relevant. As a result, we developed a new SDK, C3D B-Shaper, which is part of our C3D Toolkit.

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Total votes 6: ↑6 and ↓0 +6
Comments 0

How to Catch a Cat with TLA+

Reading time 3 min
Views 1.8K
Many programmers struggle when using formal methods to solve problems within their programs, as those methods, while effective, can be unreasonably complex. To understand why this happens, let’s use the model checking method to solve a relatively easy puzzle:

Conditions


You’re in a hallway with seven doors on one side leading to seven rooms. A cat is hiding in one of these rooms. Your task is to catch the cat. Opening a door takes one step. If you guess the correct door, you catch the cat. If you do not guess the correct door, the cat runs to the next room.
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Total votes 9: ↑9 and ↓0 +9
Comments 0

Version 12 Launches Today! (And It’s a Big Jump for Wolfram Language and Mathematica)

Reading time 47 min
Views 3.1K


Quick links


The Road to Version 12
First, Some Math
The Calculus of Uncertainty
Classic Math, Elementary and Advanced
More with Polygons
Computing with Polyhedra
Euclid-Style Geometry Made Computable
Going Super-Symbolic with Axiomatic Theories
The n-Body Problem
Language Extensions & Conveniences
More Machine Learning Superfunctions
The Latest in Neural Networks
Computing with Images
Speech Recognition & More with Audio
Natural Language Processing
Computational Chemistry
Geographic Computing Extended
Lots of Little Visualization Enhancements
Tightening Knowledgebase Integration
Integrating Big Data from External Databases
RDF, SPARQL and All That
Numerical Optimization
Nonlinear Finite Element Analysis
New, Sophisticated Compiler
Calling Python & Other Languages
More for the Wolfram “Super Shell”
Puppeting a Web Browser
Standalone Microcontrollers
Calling the Wolfram Language from Python & Other Places
Linking to the Unity Universe
Simulated Environments for Machine Learning
Blockchain (and CryptoKitty) Computation
And Ordinary Crypto as Well
Connecting to Financial Data Feeds
Software Engineering & Platform Updates
And a Lot Else…

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Total votes 9: ↑9 and ↓0 +9
Comments 0

Estimation of VaR and ConVaR for the stock price of the Kazakhstani company

Reading time 8 min
Views 1.5K

The last decades the world economy regularly falls into this vortex of financial crises that have affected each country. It almost led to the collapse of the existing financial system, due to this fact, experts in mathematical and economic modelling have become to use methods for controlling the losses of the asset and portfolio in the financial world (Lechner, L. A., and Ovaert, T. C. (2010). There is an increasing trend towards mathematical modelling of an economic process to predict the market behaviour and an assessment of its sustainability (ibid). Having without necessary attention to control and assess properly threats, everybody understands that it is able to trigger tremendous cost in the development of the organisation or even go bankrupt.


Value at Risk (VaR) has eventually been a regular approach to catch the risk among institutions in the finance sector and its regulator (Engle, R., and Manganelli S., 2004). The model is originally applied to estimate the loss value in the investment portfolio within a given period of time as well as at a given probability of occurrence. Besides the fact of using VaR in the financial sector, there are a lot of examples of estimation of value at risk in different area such as anticipating the medical staff to develop the healthcare resource management Zinouri, N. (2016). Despite its applied primitiveness in a real experiment, the model consists of drawbacks in evaluation, (ibid).


The goal of the report is a description of the existing VaR model including one of its upgrade versions, namely, Conditional Value at Risk (CVaR). In the next section and section 3, the evaluation algorithm and testing of the model are explained. For a vivid illustration, the expected loss is estimated on the asset of one of the Kazakhstani company trading in the financial stock exchange market in a long time period. The final sections 4 and 5 discuss and demonstrate the findings of the research work.

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Total votes 13: ↑13 and ↓0 +13
Comments 0

The Fall and Recovery of a Mold

Reading time 4 min
Views 1.5K
Software component developers tend to be far removed from the end users of the products in which their components are employed. Recently, however, we connected directly with a KOMPAS-3D MCAD user to solve an issue involving mold design. It seems that 3D models were being exported incorrectly to data exchange formats like STP, X_T, and SAT. The cause, unhappily for us, turned out to be in our С3D Modeler geometric modeling kernel. Here is how we solved the problem, quickly.

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Total votes 28: ↑27 and ↓1 +26
Comments 1

Kalman Filter

Reading time 9 min
Views 6.1K


There are a lot of different articles on Kalman filter, but it is difficult to find the one which contains an explanation, where all filtering formulas come from. I think that without understanding of that this science becomes completely non understandable. In this article I will try to explain everything in a simple way.

Kalman filter is very powerful tool for filtering of different kinds of data. The main idea behind this that one should use an information about the physical process. For example, if you are filtering data from a car’s speedometer then its inertia give you a right to treat a big speed deviation as a measuring error. Kalman filter is also interesting by the fact that in some way it is the best filter. We will discuss precisely what does it mean. In the end of the article I will show how it is possible to simplify the formulas.
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Total votes 21: ↑21 and ↓0 +21
Comments 1

How linear algebra is applied in machine learning

Reading time 5 min
Views 14K

When you study an abstract subject like linear algebra, you may wonder: why do you need all these vectors and matrices? How are you going to apply all this inversions, transpositions, eigenvector and eigenvalues for practical purposes?


Well, if you study linear algebra with the purpose of doing machine learning, this is the answer for you.


In brief, you can use linear algebra for machine learning on 3 different levels:


  • application of a model to data;
  • training the model;
  • understanding how it works or why it does not work.

drawing
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Total votes 49: ↑37 and ↓12 +25
Comments 39

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