Why does DES use 16 rounds?

What is theory behind it?
Here's what I did. I looked at all the cases that differ in the last 16 rounds: for example the first 4 rounds of the DES and the last 4 rounds. I found the only significant difference: in the first round of both, some bits are flipped, while others stay unchanged. In DES the flipped bits are 0. And in DES the flipped bits are -1. So, I've concluded DES uses 16 rounds to prevent being vulnerable to linear analysis.

Is this reasoning sound? So, with an attack like this, you can get a positive result for about 25% of all possible inputs.

What is an example of a DES algorithm?

A DES algorithm is a keyed encryption algorithm.

They fall into two categories: block ciphers (a name for cipher modes) and stream ciphers. All of the algorithms below are considered block ciphers, since they encrypt a block of data at a time. All of the stream ciphers described are one-time pad ciphers, which work by encrypting a random bit string with a large key, generating a random bit string that is then XOR'ed with plaintext (or another secret key), then that bit string is sent to the receiver. One-time pad ciphers are considered insecure, and if you need to encrypt something where confidentiality is a requirement, you should use a stream cipher instead. That being said, most of the block ciphers on this list are also considered one-time pad ciphers. In general, there are two types of ciphers used in modern cryptography: symmetric ciphers and asymmetric ciphers. Symmetric ciphers are used for two-way communications (think of a digital phone line, you call a number to get it ringing, then you hang up, and the phone rings), but can also be used for one-way communications (email, text messaging). Asymmetric ciphers are only used for one-way communications. The two main methods for using ciphers are key-based cryptography and non-keyed cryptography. Key-based cryptography involves keying data with a secret key, allowing for increased security and/or usability (depending on the cipher). There are a lot of block ciphers out there and they all have their pros and cons. They are often used for file encryption, because there is no limit to the length of keys, so using a huge key is not a problem. It is important to note that any ciphers designed for one-time pad crypto can be used as block ciphers. Stream ciphers are considered one-time pad ciphers. Block ciphers are one-time pad ciphers. You call the other party, they get the call, you don't have to dial a code. Asymmetric ciphers are used for one-way communications. You send an email to your friend, he receives the email, he doesn't have to read it.

What is the formula for DES?

This might be asked sooner or later.

In my experience of teaching many students, I have found that there is an order of difficulty: Calculus. Differential equations. Differential/integral equations. I am not sure which one is more important, but the first step in differentiating a product seems to be much more. Difficult than dividing two numbers. If it makes a difference, how does one get from "Differential Forms" to Linear Forms? I also understand that when solving initial value problems such as ODEs or the separable form where Dx = f(y) =0, the integration can be. Solved with the solution form. But how does one go from initial-value problems to differential equations? For some books which you should find useful are: K. Friedrichs, M. Ruzicka and H. Schulz-Baldes, Topics on Partial Differential Equations, Cambridge University Press,
Cambridge, 2026. ISBN-13: 978-0521442522 Chapter 7. Differentiation of products and functions of several variables is treated. There are exercises throughout the book.

S. Krantz, "Partial Differential Equations and Complex Variables", Second Edition, Theorem 2.3 on page 52 states that:
We know that differentiation is simply multiplication of partials by something. Later on p.63,3 on the following page: Using the result in theorem 2.3, the proof is easy.

What is the block size in DES * 1 point 56 64 128 256?

The block size in DES is defined as the number of bits you will treat as a single byte.

It is called the block size because it gives a block cipher something like the property that a block cipher (block cipher, I assume you mean) has a block size. It does not have that property, though; in DES, the block size is 56 bits, but the data it works on is 64 bits long (56 bit times two).

In terms of your question, the key size in DES is also the same as the block size. In other words, a 64-bit key is the same size as a block of data of 56 bytes.

If you were trying to answer what the block size is for DES-ECB, the block size is indeed 128 bits. The point in that algorithm is to make the block size a multiple of 64 bits. So, the key size is 56 bits, the block size is 128 bits, and the data is 56 bits times two. That's why the IV is 64 bits.