Digital television is a modern television broadcasting technology, which consists in the transmission of television sound and images using video coding. The television familiar to all of us is called analog and it is gradually disappearing into history. Its main disadvantage: signal instability in various noises and the ability to view only a few TV channels. The digital signal is immune to interference, so it provides high quality sound and picture. In addition, on one frequency, instead of an analog channel, it can transmit several digital ones at once. Thus, viewers have the opportunity to watch a variety of channels: general format, entertainment, informational, educational, children's, music, sports, broadcasting serials and films.
Benefits of digital television
According to the transmission method, digital television is divided into:
- terrestrial terrestrial television broadcasting in DVB-T2 and DVB-T modes;
- satellite and cable TV.
Benefits of connecting digital TV:
- decrease in transmitter power;
- increasing the noise immunity of television signals;
- improving the picture and sound quality in TV receivers;
- a significant increase in TV programs;
- the presence of interactive TV systems;
- availability of additional functions: "video on demand", "recording of the program", "at the beginning of the program", the choice of subtitles and language;
- the ability to create an archive of programs, etc.
The antennas used to receive the signal also differ. When buying them, you need to take into account the range of the transmitting station, line-of-sight conditions to the station, as well as the level of the transmitted signal. So, antennas with a suspension height of ten meters and a high gain, as well as indoor antennas, are considered effective. But usually the signal is successfully received on the antenna that the subscriber has been using for a long time.
So, if the issue of buying a set-top box and installing an antenna of the decimeter range has been resolved, then you can start connecting the "numbers" to your TV. To do this, we connect the tuner to the TV according to the instructions that come with it. Then we connect the antenna to it and use the remote control to start the channel search procedure. The search can be carried out manually or automatically (choose the one that suits you). After a few minutes, the result will appear on the screen. Note, it is quite simple to find out if your TV supports digital television. So, if it has the designation DVB-T2, then it receives digital terrestrial television; if DVB-S - then it receives satellite TV and DVB-C - cable.
Before installing digital television, be sure to find out where the transmitting tower is located. You will need to direct the antenna in its direction. If an external antenna is used, it must be securely attached to the brackets.
Even those accountants who have been submitting reports via the Internet for a long time do not always understand how one of the main elements of the reporting system - an electronic digital signature (EDS) - works. Meanwhile, such knowledge allows one to prevent some elementary mistakes that can lead to conflicts with the inspection. In addition, an accountant who has received an understanding of the basics of digital signature technology will spend much less time communicating with call center operators.
EDS creation
There are different ways to generate an electronic digital signature. In practice, the most convenient and common way is to create an EDS using two keys - public and private. Both of these keys are created using a special encryption program (for example, "Crypto-Pro"). To create a private key, you must either move the mouse chaotically, or haphazardly press keys on the keyboard. The program converts these movements into a very long character set (its size is 512 bits; about whether it is a lot or a little - below, in the "Additional Information" section). This creates a private key.
Then the same program, based on the private key, creates a public key (just note that the reverse process - picking up a private key using a public key - is impossible). The public key is published on the websites of certification centers and a special communication operator, whose services are used by the owner of the key, but the private key should be stored with all possible precautions.
Why do you need certification centers
They solve the most important task: they confirm the authenticity of information about the owner of the key and his powers. If the CA did not exist, anyone who bought an encryption program could declare their public key as the key of the chief accountant of Gazprom or the head of the inspectorate for the largest taxpayers.
Therefore, an accountant (manager), in order to issue an electronic digital signature, must provide the CA with documents proving his identity, a power of attorney from the company and write a request for the issuance of a public signature key certificate. The Center issues electronic and paper certificates of the signature public key. An electronic certificate is a file that is a client's public key, signed by a digital signature of a certification center. A paper certificate contains the following data: EDS public key, full name of its owner, certificate validity period (usually one year), key scope (a list of documents that can be signed using the key for which the certificate is issued), information about the organization whose representative is the owner of the key.
Accordingly, after processing the documents in the CA, the client has a paper certificate and a storage medium (ru-token, flash drive, floppy disk) on which the following files are recorded: public key, private key, public key certificate.
We encrypt open, decrypt closed
Let's say an accountant wants to send a declaration to the inspection. He generates a file with reporting (enters the organization's data in the electronic declaration format). He then signs the reporting file with his private key. The signing forms a new, original file. In a document signed with an EDS, neither the recipient nor the sender can change a single character - such a violation of the integrity of the document is easily detected during verification using a public key certificate.
Further, the program with which the accountant sends reports, encrypts the declaration with the public key of the inspection. The encrypted file is sent to the inspection. The tax authorities receive the file and decrypt it with their private key. Then the payer's EDS is checked using the register of public key certificates (such a check is carried out automatically when receiving reports). The check gives an answer to two questions: whether the integrity of the document was violated after signing the payer's EDS and whether this EDS really belongs to the payer who submitted the reporting.
After verification, the inspection sends the organization an incoming control protocol. The inspector signs the protocol with his private key. Then it encrypts the protocol with the company's public key and sends the file with the encrypted information to the company's address. The accountant opens the information encrypted in the file with his private key.
In theory, anyone can intercept an encrypted file. However, you can decrypt the file sent to the inspection address only if you have the inspection's private key. Accordingly, an encrypted file sent to a company can only be opened by someone who has the company's private key.
What happens if you carelessly store a private key
The most important problem that a careless storage of a private key can pose for a company is the so-called key compromise. That is, access to the private key by outsiders. If the key is stored on a floppy disk on the accountant's desk or the key is written to the hard disk of an accounting computer, then the company runs the risk of running into serious trouble. Having a private key, some ill-wisher can send deliberately false reporting for the company. For example, long before the deadline for which the accountant plans to submit reports, send a VAT declaration with huge amounts to be refunded to the inspectorate. In this case, the company will at least face a tedious litigation with the tax authorities, who have already accepted the "false" reporting and entered it into their database. And as a maximum (if the accountant does not find out the fact of "false" sending in time) - the reclamation of documents in the course of an in-depth desk audit, additional charges, penalties, fines and legal proceedings.
Another consequence of careless storage is the potential loss of the private key. The key can be stolen. You can lose it. If the private key is written on an unreliable medium - a floppy disk, there is a danger of its mechanical damage. In addition, a floppy disk can get lost among other floppy disks, and information from it can be erased by mistake.
The loss of a valid key on the eve of the submission of reports leads to the fact that it will not be possible to send the declaration on time via the Internet. The fact is that no one will be able to give the organization a "duplicate" of the private key - the certification authority simply does not have one, and it is impossible to recreate the private key from the public key. Without a private key, the company will not be able to sign the statements and decrypt the protocols from the inspection, where it is reported whether the statements were accepted or not accepted due to some errors. The only way out is to get new keys. If this procedure is delayed, and the inspectorate takes note of the information about the new keys with a delay, the declarations will have to be submitted in person or sent by ordinary mail.
Private keys that have expired should also be stored with care. This thesis is especially relevant for accountants who store all submitted reports not on their own computer, but in encrypted form on the server of the communications operator. If they lose the private key that was in force, say, in 2006, then they will not be able to decipher their own tax records for that year.
Additional Information
How reliable is EDS
As we have already mentioned, the size of the EDS private key used when submitting reports is 512 bits. In order to understand the degree of reliability provided by such a key size, we will give an example. It took a team of researchers three years to find a 72-bit key, using hundreds of computers. Our key size is 512 bits. The conditions of the experiment carried out make it possible to calculate the number of years it will take to select it. This term is expressed as a number with 130 zeros. For comparison: the age of the Earth is estimated at 4.5 billion years, and a billion is a number with 9 zeros.
How does EDS differ from old encryption
One of the first to use encryption of information (cryptography) in practice was the emperor Gaius Julius Caesar. He sent messages to remote provinces, where instead of the letter A he put the letter D, instead of the letter B - the letter E, etc. That is, he used an alphabetical shift by three letters. This was enough so that the enemies who intercepted the message could not decipher it. But the addressees in the provinces, who knew the secret of the cipher, easily read the orders from the capital.
More than two thousand years have passed since then. During this time, a huge number of ciphers were invented (for Caesar, this was the simplest alphabetical shift by 3 letters, and creepy thousand-digit numbers were already used in the scrambler devices of the Second World War). However, until recently, the science of encryption did not invent anything fundamentally new. The essence remained the same: before the document flow session, the sender of the message and its recipient had to share the secret of the cipher (which required either a personal meeting or the use of some ultra-reliable communication channels). Such encryption, in which the participants in the workflow need to transfer the cipher secret to each other, is called symmetric cryptography.
However, in the seventies of the last century, a fundamentally new method of cryptographic protection of information was invented. It does not require a preliminary exchange of the cipher secret, which is why it was called asymmetric cryptography. It is this encryption method that is used in the work of an EDS. To send encrypted information to someone, it is enough to have EDS keys yourself and know the recipient's public key.
Looking around you, you will most likely see on your desk, or not far from it, a laser or inkjet printer, which you use to create various kinds of documents that you need for work and in everyday life. Having made a real revolution in the world of printing a couple of decades ago, digital printers have gained immense popularity, which is growing every day, becoming a worthy competitor to offset printing machines.
In the early years of digital printing equipment, even an inexperienced person could distinguish documents printed on digital machines from materials created using offset equipment - it gave out quality. But the development of digital machines did not stand still, actively developing, and today they have reached a level at which they are able to show excellent quality of printed products.
Today, the difference between digital printing and offset printing is that each of these types of printing can be used for the implementation of certain purposes, taking into account the advantages and disadvantages of different equipment for each of them.
The term "digital printing" is broad enough to include any method of reproduction of documents using electronic files, dots that form images, ink or toner, depending on what kind of digital equipment is used. Due to the fact that a digital printer reproduces a page image in accordance with a specific print job, and does not transfer the print onto paper using special plates, the images printed by digital equipment may be different for each next printed sheet. The digital printer does not require installation of sheets for printing various graphic and text elements.
Benefits of digital printing
Due to the peculiarities of applying elements on paper with digital printers, they are able to solve two very important tasks: printing multi-page materials within one print job and allowing you to create personalized printed materials, which is especially necessary when you want to contact personally a particular company or a specific to the consumer. This feature opens up great opportunities for the marketing steps of any enterprise. In addition, digital equipment allows you to print materials in a short time.
Digital printing - how does it work?
The digital printing process begins with the creation of a document file, which will include the text and images reproduced in the document. Regardless of what software is used to create the file and any of the elements, the file with a graphic image must be a bitmap. The raster grid is located on the x and y axes, and when working with a file, it is determined which of them is to be processed.
A raster image file is sometimes called a bitmap because it contains information that is directly involved in the formation of the mesh. BMP, TIFF, GIF, and JPEG are examples of bitmap image file types. Converting a file to a bitmap file is called bitmap processing. When preparing files for printing, all of them must be copied to create a bitmap, from which the data will be taken to print the image by applying dots to the right places.
Digital printers can use different technologies depending on the substance through which the images are applied to the paper (toner or ink). Dry toner is most commonly used for printers.
How does a laser printer work?
Laser printers use pulses of light from a laser beam to be displayed on a light-sensitive surface. Images are formed from dots in Matrix, as a rule, 600x600 dots per inch, 750x750 dots / cm or 1500x1500 dots / cm.
A laser printer uses technology similar to that of a copier, based on the principle of attraction of opposite electric charges. Using the bitmap information from the copied file, the laser beam delivers an electrically charged photoreceptor. Toner particles are attracted to it and then transferred to the paper. Toner fuses to the paper as it passes through the hot rollers (approximately 400 degrees).
The high temperature required to fix the toner on the paper imposes some limitations on the types of paper that can be used for laser printers.
Toner
The toner particles are negatively charged, on the plastic bases there is a powder that heats up under temperature. The toner consists of a colored or black pigment and a polymer. The mixture is heated and crushed and then cooled. Heating creates toner particles ranging in size from 7 to 10 microns.
The size of the toner particle affects the resolution of the printed image. The number of points must match the points in the bitmap. This is important to reproduce images at normal resolution.
How does an inkjet printer work?
An inkjet printer uses very small droplets of ink to reproduce images on paper. The ink droplets are controlled by a digital signal to spray the liquid ink onto the paper. The inkjet ink droplet size is approximately 50-60 microns, i.e. these droplets are smaller than the diameter of a human hair (70 microns), but larger than the toner particles.
When printing photographs, an inkjet printer produces high quality images that are close to photographic ones. Inkjet printers work with paper and other substrates, including roll paper. This allows you to print large-format materials in high resolution.
Digital printing and paper
Paper intended for digital printing has different properties than paper used for offset printing. In particular, the paper must be heat-resistant, not changing its qualities when exposed to high temperatures, pressure and chemical elements that make up the toner.
You may have encountered ink leakage or other difficulties when printing materials on inkjet equipment. Printing with toner may cause problems such as ink particles being printed onto objects and other papers when the sheet is still warm after printing. This means that the paper selected for printing is not suitable for work with digital equipment.
Why do you need to know about the features of digital printing presses?
Having knowledge of the principles of digital equipment operation is necessary so that, in cooperation with a printing house that will print various kinds of materials for you, you can navigate in recommendations and advice from its employees, choose the right paper and other consumables for your work.
> How does a digital camera work
A digital camera captures light and focuses it through a lens onto a sensor made of silicon. It consists of a grid of small photocells that are sensitive to light. Each photocell is called a pixel, short for picture element. Millions of these individual pixels reside in the sensor of a digital SLR.
A digital camera selects the light of our world, or outer space, spatially, tonally and in time. Spatial sampling means that the image in the camera is split into a rectangular grid of pixels. Tonal sampling means that constantly changing luminance tones in nature are broken up into discrete discrete tone steps. If there are enough samples, both in space and tonal, we perceive them as a correct representation of the original scene. Sampling time means that we are making an exposure for a given duration.
Our eyes also perceive the world on a basis of a few tenths of a second when the amount of light is the same as during daytime. In low light conditions, eye exposure, or integration time can increase to several seconds. This is why we can see more detailed information with a telescope if we look at a faint object for a long time.
The eye is a relatively sensitive detector. It can detect one photon, but this information is not transmitted to the brain because it does not exceed the minimum signal-to-noise ratio threshold in the noise filtering scheme in the visual system. This threshold causes the entry of several photons to be fixed by the brain. A digital camera is almost as sensitive as the eyes, and both are much more sensitive than film, which requires many photons to be detected.
These are long exposure time samples that really make the magic of digital astrophotography possible. The true power of a digital sensor comes from its ability to integrate, or collect, photons over longer periods of time than the eyes. This is why we can record long exposures that are invisible to the eye, even through a large telescope.
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Each light-sensitive element on a CCD or CMOD chip consists of a crystalline silicon light-sensitive area in a photodiode that absorbs photons and releases electrons through the photoelectric effect. Electrons accumulate in the potential well as an electrical charge that builds up over the entire exposure. The charge that is generated is proportional to the number of photons that hit the sensor. This electrical charge is transferred and converted into an analog voltage, which is amplified and then sent to an analog-to-digital converter, where it is digitized (converted into a number). |
CCD and CMOD sensors work similarly to each other in absorbing photons, generating electrons and storing them, but differ in how charge is transferred and where it is converted into voltage. And both have digital output.
The entire digital image file is a collection of numbers that represent the brightness and location values for each square in the array. These numbers are stored in a file that our computers can work with.
Not all pixels are light sensitive, only photodiode ones. The percentage of pixels that are light-sensitive is called the duty cycle. For some sensors, such as CMOD, the duty cycle can be only 30 to 40 percent of the total area of the photocells. The rest of the area on the CMOD sensor consists of electronic circuits such as amplifiers and noise canceling circuits.
Since the light-sensitive area is small compared to the pixel size, the overall sensitivity of the chip decreases. To increase the fill factor, manufacturers use micro-lenses to direct photons, which hit non-sensitive areas and go unnoticed, onto the photodiode.
Electrons are generated as long as photons strike the sensor for the duration of exposure or integration. They are stored in a potential pit until the end of the irradiation. The size of the well is called the total capacity, and it determines how many electrons can be collected before the well is full and registered in full. In some sensors, after filling one well, electrons can spill over to adjacent wells, causing blooming, which is seen as vertical peaks on bright stars. Some cameras have anti-alumina capabilities to reduce or prevent this phenomenon. Most DSLR cameras control blooming very well and this is not a problem for astrophotography.
The amount of electrons that can accumulate in the well determines the dynamic range of the sensor and also the black to white brightness range where the camera can record details in both faint and bright areas of a scene. After noise correction, a sensor with a higher capacitance usually has a higher dynamic range. A low noise sensor helps improve dynamic range and enhances detail in low light areas.
Not every photon that hits the detector will be detected. The amount to be recorded is determined by the quantum efficiency of the sensor. Quantum efficiency is measured as a percentage. If the sensor has a quantum efficiency of 40 percent, this means that four out of every ten photons that hit the sensor will be registered and converted into electrons. According to Roger N. Clarke, the quantum efficiency in modern digital SLR cameras ranges from 20 to 50 percent, depending on the wavelength. Top-of-the-line astronomical CCD cameras can have quantum efficiencies of up to 80 percent or more, although this applies to grayscale images.
The number of electrons collected in the well is proportional to the number of photons that are registered. The electrons in the well are then converted to voltage. This charge is an analog signal (continuously changing) and is usually very small and must be amplified before it can be digitized. The output amplifier performs this function by matching the output voltage range of the sensor to the input voltage range of the AD converter. The AD converter converts this data to a binary number.
When the AD converter digitizes the dynamic range, it splits it in steps. The total number of steps is given by the bit depth of the transducer. Most DSLR cameras operate at 12-bit (4096 steps) tonal depth.
The sensor output is technically referred to as an analog-to-digital unit (ADU) or digital number (DN). The number of electrons in an ADU is determined by the system gain. Gain of 4 means that the AD converter digitizes the signal so that each ADU corresponds to 4 electrons.
The ISO exposure class corresponds to the film speed class. This is a general assessment of light sensitivity. The digital camera sensors only have one sensitivity, but allow different ISO settings by changing the camera gain. When the gain is doubled, the number of electrons in the ADU is halved.
By increasing the ISO in a digital camera, fewer electrons are converted into one ADU. Raising the ISO decreases the dynamic range. At ISO 1600, only about 1/16 of the full potential well of the sensor can be used. This can be useful for astronomical images of faint objects from which electrons cannot be collected in any other way to fill the potential well. The camera only converts a small number of electrons from these rare photons and maps this limited dynamic range to the full bit depth, making large differentiation between steps possible. It also gives more steps to work with this weak data when it is stretched later in processing to increase contrast and visibility.
For each pixel in the sensor, luminance data, represented by a number between 0 and 4095 for a 12-bit AD converter, along with the coordinates of the pixel's location, is stored in a file. This data can be temporarily stored in the camera's built-in buffer memory before being written to the camera's removable memory card.
This file of numbers is reconstructed into an image when displayed on a computer monitor or printed.
These are the numbers that are produced in the digitization process, with which we can work on our computers. Numbers are represented as bits, and are represented as "binary digits". Bits use base 2 in binary, where there are only digits one and zero, not base 10, where there are digits from 0 to 9, which is what we tend to work with. Computers use binary numbers because the transistors they are made of have only two states, on and off, which are represented by the numbers one and zero, respectively. All numbers can be represented this way. This is what makes computers so powerful at dealing with numbers, transistors do it very quickly.
Spatial sampling
The photosensitive element in the camera's sensor is matched one-to-one with the pixels in the digital image when it is output. Many people also refer to such elements in the camera matrix by the generic term "pixels". These elements are arranged in a rectangular array. In the Canon 20D, the array is 3504 x 2336 pixels, for a total of 8.2 million pixels. This grid can be thought of as a chessboard where each square is very small. The squares are so small that when viewed from a distance, they make the eye and brain think the image is continuous. If you enlarge any digital image to a large enough size, you can see individual pixels. When this happens, we call the image "fuzzy".
A color image is actually made up of three separate channels, one each for red, green, and blue. Because of the way the eye and the brain perceive color, all the colors of the rainbow can be created from these three primary colors.
Although a digital camera can record 12-bit or 4096 steps of information luminance, almost all output devices can only display 8-bit or 256 steps per color channel. The original 12-bit (2 to 12 power = 4096) input must be converted to 8 bit (2 to 8 power = 256) data for output.
In the above example, the nominal pixel has a luminance level of 252 in the red channel, 231 in the green channel, and 217 in the blue channel. The brightness of each color can range from 0 to 255, with 256 total steps in each color channel when displayed on a computer monitor, or for output on a desktop printer. Zero means pure black and 255 indicates pure white.
The 256 colors each of red, green and blue may not seem like a lot, but it's actually a huge number, because 256 x 256 x 256 are over 16 million individual colors.
Tonal sampling
The lights and tones in the world change in a continuous manner. After sunset on a clear day, the sky in the west ranges from bright near the horizon to deep blue overhead. These shades of blue are constantly changing. They smoothly transition from light to dark.
When measuring light, digital cameras break its continuously changing signals into discrete steps that can be represented by numbers (numbers). They digitize the image.
64 steps
32 steps
16 steps
Thanks to the way our visual system uses it, if we separate continuous signals in enough small discrete steps, we can trick the eye into thinking that it is a continuous signal, even if it is not.
In the examples above, we can see the effect of a different number of tones when we go from black to white. We can clearly differentiate a small number of tones as discontinuities. But when the number increases, somewhere around 128 steps, they seem to be continuous to our perception.
Computers and numbers
Since the computer is a very powerful tool for manipulating numbers, we can perform various operations on these numbers quickly and easily.
For example, contrast is defined as the difference in brightness between adjacent pixels. For contrast, there must be a difference, so that one pixel is brighter and the other pixel is darker. We can increase the contrast very easily by simply adding the number of steps in brightness for the bright pixel and subtracting the number of steps from the brightness value of the dark pixel.
Color in an image is represented by the luminance value of a pixel in each of the three color channels — red, green, and blue — that make up color information. We can just as easily change the color of a pixel, or a group of pixels, simply by changing the number.
We can do other tricks, such as increasing the apparent sharpness of an image by increasing the contrast of the edge edges of objects in the image using a process called unsharp masking.
Representing an image as a number allows us to have complete control over it. And, since the image is a collection of numbers, it can be duplicated any number of times without loss of quality.
Linear or non-linear data
The response of a digital sensor recording is proportional to the number of photons that hit it. The response is linear. Unlike photographic film, digital sensors double the recorded signal when the number of photons hitting the sensor doubles. Digital sensors are also interchangeable like most photographic films.
The data captured by the CMOS sensor in a digital SLR and recorded in the raw file is linear. Linear data tends to appear very dark compared to normal photographs (see illustration below).
Linear curve
Human visual perception of brightness is better described by a logarithmic curve than by a linear curve. Other human senses, such as hearing, and even taste, are also logarithmic. This means that we are better at distinguishing differences at the lower end of the perceptual scale than we are at the high end. For example, we can very easily distinguish between one pound and two pounds by weight when we lift them. But we have difficulty trying to distinguish between 100 pounds and 101 pounds. However, the difference is the same, one pound.
Logarithmic curve
Normal photographs on film are also recorded in a non-linear manner that is similar to the way humans perceive it. This is why we can hold the slide towards the light and it looks like a reasonable representation of the original scene without any additional modifications.
Due to the fact that the human visual perception system does not work in a linear fashion, a nonlinear law must be applied when stretching linear data from a DSLR camera to better match the tonality of the photographs with our visual perception. These non-linear corrections are made with software inside the camera when the image is recorded as a JPEG file. If the raw file is saved in the camera, these non-linear adjustments are made in the software later when the data is opened in an imaging program.
In the sample images shown above, a screenshot of the Curves dialog in Photoshop has been included in the image so that we can see a comparison between linear data and the same non-linearly adjusted data. The curve in the dark image is linear, that is, a straight line. The curve in the light image is shown with a stretch that needs to be applied to the data to make it closer to our visual perception.
The curve represents the input and output brightness values of the pixels in the image. Black in the lower left corner and white in the upper right corner. Gray tones in between. When the line is straight, an input that runs horizontally along the bottom corresponds to an output that runs vertically along the left side.
The inset shows that when a straight line is pulled upward so that its slope increases, the contrast of that portion of the curve and the corresponding tones in the image increases. In the example above, you can see that the tone at this point is much easier to create. All tones in the image below this point on the curve, and the corresponding tones in the image, are stretched from each other and their contrast has increased.
This is why it is important to work with a high bit depth when working with raw images. Due to the strong tension and increased contrast that are needed, the tones are stretched. If we have a lot of tones and the depth of the high tone allows, then they can be smoothly redistributed. If we have few tones to work with, we run the risk of getting posterization and stripes when stretching the data.
In a bright image, the slope of the top of the curve decreases in the lighter areas of the image. This compresses the tones and reduces the contrast of those tones in the image.
This is what allows this data to be accessed in linear form at a high bit depth, which makes DSLR and CCD images so powerful for astrophotography. This allows us to subtract the sky background and light pollution. This gives us the ability to control non-linear adjustments and stretch the data. These settings bring out the details of astronomical objects that are buried deep in what we think of as shadow areas in normal photography.
Electronic digital signatures are now common knowledge - many modern companies are slowly switching to electronic document management. Yes, and in everyday life, you probably came across this thing. In a nutshell, the essence of an EDS is very simple: there is a certification center, there is a key generator, a little more magic, and voila - all documents are signed. It remains to figure out what kind of magic allows a digital signature to work.
Roadmap
This is the fifth lesson in the Crypt Dive series. All lessons of the cycle in chronological order:
1. Generation of keys
The reason RSA is strong is the difficulty of factoring large numbers. In other words, it is very difficult to brute force to find such primes that give the modulus n in the product. Keys are generated in the same way for signature and encryption.
When the keys are generated, you can start calculating the electronic signature.
2. Calculation of electronic signature
3. Verification of electronic signature
RSA is known to be about to retire because computing power is growing by leaps and bounds. The day is not far off when a 1024-bit RSA key can be found in minutes. However, we will talk about quantum computers next time.
In general, you should not rely on the strength of this RSA signature scheme, especially with keys as strong as in our example.
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