## Hilberts tenth problem

Hilberts tenth problem is a problem in mathematics that is named after David Hilbert who included it in Hilberts problems as a very important problem in mathematics. It is about finding an algorithm that can say whether a Diophantine equation has ...

## Hyperoperation

A hyperoperation is a generalization of addition, multiplication, exponentiation, tetration, etc. They are often written using Knuths up-arrow notation. Natural number level hyperoperations can be defined recursively as a piecewise function: H n ...

## Icosagon

The amount of space a regular icosagon takes up is Area = 5 a 2 1 + 5 + 5 + 2 5. {\displaystyle {\text{Area}}={5}a^{2}1+{\sqrt {5}}+{\sqrt {5+2{\sqrt {5}}}}.} a is the length of one of its sides.

## Icosahedron

An icosahedron is a Platonic solid that is made of triangles and has twenty sides. There are many kinds of icosahedra, with some being more symmetrical than others. The best known is the Platonic, convex regular icosahedron.

## Implicit derivative

Implicit derivatives are derivatives of implicit functions. This means that they are not in the form of y = f {\displaystyle y=f}, and are instead in the form 0 = f {\displaystyle 0=f}. It might not be possible to rearrange the function into the ...

## Internet Key Exchange

Internet Key Exchange is the protocol used to set up a security association in the IPsec protocol suite. IKE uses a Diffie-Hellman key exchange to set up a shared session secret, from which cryptographic keys are derived. Public key techniques or ...

## Invertible matrix

In linear algebra, there are certain matrices which have the property that when they are multiplied with another matrix, the result is the identity matrix I {\displaystyle I}. If A {\displaystyle A} is such a matrix, then A {\displaystyle A} is c ...

## Irrational number

In mathematics, an irrational number is a real number that cannot be written as a complete ratio of two integers. An irrational number cannot be fully written down in decimal form. It would have an infinite number of digits after the decimal poin ...

## Isosceles triangle

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having two and only two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus i ...

## Key (cryptography)

In cryptography, a key is a piece of information that allows control over the encryption or decryption process. There are two basic types of cryptographic algorithms. Symmetric algorithm: If there is just one key for encrypting and decrypting, th ...

## Key exchange

Key exchange is any method in cryptography by which cryptographic keys are exchanged between users, allowing use of a cryptographic system. If two parties wish to exchange encrypted messages, each needs to know how to decrypt received messages an ...

## Key generation

Key generation is the process of generating keys for cryptography. The key is used to encrypt and decrypt data whatever the data is being encrypted or decrypted. Modern cryptographic systems include symmetric-key algorithms such as DES and AES an ...

## Key schedule

In cryptography, the so-called product ciphers are a certain kind of ciphers, where the decryption of data is done in "rounds". The general setup of each round is the same, except for some hard-coded parameters and a part of the cipher key, calle ...

## Key size

In cryptography, key size or key length is the size of the key used in a cryptographic algorithm. Typical key sizes in modern symmetric ciphers are 128, 192, and 256 bits. Older symmetric ciphers used only 40, 56, or 64 bits, which can be broken ...

## Key space

In cryptography, the key space of an algorithm refers to the set of all possible keys that can be used to initialize the cryptographic algorithm. For example, if an algorithm works using a key that is a string of 10 bits, then its key space is th ...

## Keystream

In cryptography, a keystream is a stream of random or pseudorandom characters that are combined with a plaintext message to produce an encrypted message. The "characters" in the keystream can be bits, bytes, numbers or actual characters like A-Z ...

## Known-plaintext attack

The known-plaintext attack is an attack model for cryptanalysis where the attacker has samples of both the plaintext and its encrypted version then they can use them to expose further secret information after calculating the secret key. Encrypted ...

## Knuths up-arrow notation

Knuths up-arrow notation is a way of expressing very big numbers. It was made by Donald Knuth in 1976. It is related to the hyperoperation sequence. The notation is used in Grahams number. One arrow represents exponentiation, 2 arrows represent t ...

## Linear algebra

Linear algebra is a branch of mathematics. It came from mathematicians trying to solve systems of linear equations. Vectors and matrices are used to solve these systems. The main objects of study currently are vector spaces and linear mappings be ...

## Linear cryptanalysis

In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of the two mo ...

## Linear independence

Linear independence is a concept from linear algebra. It is used to talk about vector spaces. Each vector space has a null vector. This vector is expressed as a linear combination of other vectors. A set of these vectors is called linearly indepe ...

## MacGuffin (cipher)

In cryptography, MacGuffin is a block cipher created in 1994 by Bruce Schneier and Matt Blaze at a Fast Software Encryption workshop. It was intended as a catalyst for analysis of a new cipher structure, known as Generalized Unbalanced Feistel Ne ...

## MD5

MD5 is a special algorithm, a mathematical process, used to make computer information secure and safe. MD5 stands for M essage D igest, and was made to replace the MD4 standard. It is mainly used for security in database systems. The algorithm ge ...

## Meet-in-the-middle attack

The Meet-in-the-middle attack is a cryptographic attack which, like the birthday attack, makes use of a space-time tradeoff. While the birthday attack attempts to find two values in the domain of a function that map to the same value in its range ...

## Merge sort

Merge sort is an divide and conquer algorithm for sorting a list of elements. John von Neumann first presented it in 1945. The algorithm is pretty simple: Apply the algorithm to each of the two lists Divide the list of elements into two lists, of ...

## Mersenne prime

In mathematics, a Mersenne number is a number that is one less than a power of two. M n = 2 n − 1. A Mersenne prime is a Mersenne number that is a prime number. This however, is not sufficient. Many mathematicians prefer the definition of a Merse ...

## Mile

The nautical mile is used for sea or air travel. The nautical mile was originally defined as one minute of arc along a line of longitude of the Earth. There are 60 minutes of arc in one degree or arc 60 = 1°. So there were 10.800 nautical miles f ...

## Modular exponentiation

Modular exponentiation is about finding the value of the equation c = b e mod m. This is the remainder when dividing b e by m. It is the inverse function of the discrete logarithm. Because modular exponentiation is easy and fast, and finding the ...

## MQV

MQV is an authenticated protocol for key agreement based on the Diffie-Hellman scheme. MQV provides protection against an active attacker.

## Multiple integral

In calculus and mathematical analysis, an integral is a way to calculate the limiting value a function with one variable will tend towards. Graphically, this can then be shown as the area under the graph of the function. In multivariate calculus, ...

## Nanometre

The nanometre is a unit used to measure length in the metric system. It is equal to one billionth of a metre. The name combines the SI prefix nano- with the parent unit name metre. It can be written in scientific notation as 1×10 −9 m. The nanome ...

## Natural number

Natural numbers, also called counting numbers, are the numbers used for counting things. Natural numbers are the numbers small children learn about when they first started to count. Natural numbers are always whole numbers and often exclude zero, ...

## Newton (unit)

The newton is the SI unit of force. It is named after Sir Isaac Newton because of his work on classical mechanics. A newton is how much force is required to make a mass of one kilogram accelerate at a rate of one metre per second squared. 1 N = 1 ...

## Nonagon

The amount of space a regular nonagon takes up is A = 9 4 a 2 cot ⁡ π 9 = 9 / 2 a r = 9 r 2 tan ⁡ π / 9 {\displaystyle A={\frac {9}{4}}a^{2}\cot {\frac {\pi }{9}}=9/2ar=9r^{2}\tan\pi /9} = 9 / 2 R 2 sin ⁡ 2 π / 9 ≃ 6.18182 a 2. {\displaystyle =9/ ...

## Octahedron

An Octahedron is a polyhedron made of eight faces. in the case of the regular octahedron, these faces are triangles. The ocahedron looks like two pyramids, which share the same base. In chemistry, octahedra are common: diamonds and fluorite are e ...

## Odd abundant number

The first example is 945 3 × 5× 7. Its prime factors are 3, 5, and 7. The next following eleven odd abundant numbers are 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615. Odd abundant numbers below 500000 are in On-Line Encycloped ...

## Ordinal number

Ordinal numbers are numbers that show somethings order, for example: 1st, 2nd, 3rd, 4th, 5th. Suppose a person has four different T-shirts, and then lays them in front of the person, from left to right. Right of that is the blue one. And finally, ...

## Palindromic prime

A palindromical prime number is a prime number that reads the same when reversed. Palindromical prime numbers include: 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 1 ...

## Parabola

The parabola is a type of curve. Menaechmus discovered the parabola, and Apollonius of Perga first named it. A parabola is a conic section. If a cone is dissected by a plane which is parallel to one of the surfaces of the cone, the result is a pa ...

## Parallelogram

A parallelogram is a polygon with four sides. It has two pairs of parallel sides and four edges. The opposite sides of a parallelogram have the same length. The word "parallelogram" comes from the Greek word "parallelogrammon". Rectangles, rhombu ...

## Pentacontagon

One interior angle in a regular pentacontagon is 172​ 4 ⁄ 5 °, meaning that one exterior angle would be 7​ 1 ⁄ 5 °. The area of a regular pentacontagon is with t = edge length A = 25 2 t 2 cot ⁡ π 50 {\displaystyle A={\frac {25}{2}}t^{2}\cot {\fr ...

## Pentagon

A pentagon is a polygon with five edges. It is defined by five points, which are all on a plane. If all the edges have the same length and the angles at the corners are all 108°, the pentagon is called regular. Pentagons also occur in nature: Fru ...

## Platonic solid

A platonic solid is a kind of polyhedron. It has the following characteristics: There are the same number of polygons meeting at every corner of the shape. Each face is built from the same type of polygons

## Poisson distribution

In probability and statistics, Poisson distribution is a probability distribution. It is named after Simeon Denis Poisson. It measures the probability that a certain number of events occur within a certain period of time. The events need to be un ...

## Polygon

A polygon is a closed two-dimensional shape. It is a simple curve that is made up of straight line segments. It usually has three sides and three corners or more. It could also be referred to as A closed plane figure bound by three or more straig ...

## Polyhedron

A polyhedron is a geometrical shape. It is a 3D shape with flat faces, and straight edges. Each face is a polygon surrounded by edges. Usually it is defined by the number of faces, or edges. Two types of polyhedron are convex and concave. The lin ...

## Polynomial remainder theorem

The polynomial remainder theorem states that: for every polynomial P x {\displaystyle Px} and every real number a {\displaystyle a} the remainder of division of P x {\displaystyle Px} by x − a {\displaystyle x-a} is P a {\displaystyle Pa}. This t ...

## Pre-shared key

In cryptography, a pre-shared key or PSK is a shared secret which was previously shared between the two parties using some secure channel before it is used. Such systems almost always use symmetric key cryptographic algorithms. The characteristic ...

## Primality test

A primality test is a method to find out if a certain number is a prime number. Cryptography uses prime numbers, and needs to test if a certain number is prime. The official proof of a prime is through its primality certificate.

## Prime factorization

Prime factorization of any given number is to breakdown the number into its factors until all of its factors are prime numbers. This can be achieved by dividing the given number from smallest prime number and continue it until all its factors are ...