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The XTR public key system

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Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod p when p is a prime number. The order of a finite field is its number of elements, which is either a prime number or a prime power.

Security bug

A security bug or security defect is a software bug that can be exploited to gain unauthorized access or privileges on a computer system. Security bugs introduce security vulnerabilities by compromising one or more of: Authentication of users and other entities Authorization of access rights and privileges Data confidentiality Data integrity Security bugs do not need be identified nor exploited to be qualified as such and are assumed to be much more common than known vulnerabilities in almost any system.

Exploit (computer security)

An exploit (from the English verb to exploit, meaning "to use something to one’s own advantage") is a piece of software, a chunk of data, or a sequence of commands that takes advantage of a bug or vulnerability to cause unintended or unanticipated behavior to occur on computer software, hardware, or something electronic (usually computerized). Such behavior frequently includes things like gaining control of a computer system, allowing privilege escalation, or a denial-of-service (DoS or related DDoS) attack.

Computer security

Computer security, cyber security, digital security or information technology security (IT security) is the protection of computer systems and networks from attacks by malicious actors that may result in unauthorized information disclosure, theft of, or damage to hardware, software, or data, as well as from the disruption or misdirection of the services they provide. The field is significant due to the expanded reliance on computer systems, the Internet, and wireless network standards such as Bluetooth and Wi-Fi.

Finite ring

In mathematics, more specifically abstract algebra, a finite ring is a ring that has a finite number of elements. Every finite field is an example of a finite ring, and the additive part of every finite ring is an example of an abelian finite group, but the concept of finite rings in their own right has a more recent history. Although rings have more structure than groups, the theory of finite rings is simpler than that of finite groups.

Threat (computer)

In computer security, a threat is a potential negative action or event facilitated by a vulnerability that results in an unwanted impact to a computer system or application. A threat can be either a negative "intentional" event (i.e. hacking: an individual cracker or a criminal organization) or an "accidental" negative event (e.g. the possibility of a computer malfunctioning, or the possibility of a natural disaster event such as an earthquake, a fire, or a tornado) or otherwise a circumstance, capability, action, or event.

Cloud computing security

Cloud computing security or, more simply, cloud security, refers to a broad set of policies, technologies, applications, and controls utilized to protect virtualized IP, data, applications, services, and the associated infrastructure of cloud computing. It is a sub-domain of computer security, network security, and, more broadly, information security. Cloud computing and storage provide users with the capabilities to store and process their data in third-party data centers.

Multiplicative group

In mathematics and group theory, the term multiplicative group refers to one of the following concepts: the group under multiplication of the invertible elements of a field, ring, or other structure for which one of its operations is referred to as multiplication. In the case of a field F, the group is (F ∖ {0}, •), where 0 refers to the zero element of F and the binary operation • is the field multiplication, the algebraic torus GL(1).. The multiplicative group of integers modulo n is the group under multiplication of the invertible elements of .

Multiplicative group of integers modulo n

In modular arithmetic, the integers coprime (relatively prime) to n from the set of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n. Hence another name is the group of primitive residue classes modulo n. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n.

Finite field arithmetic

In mathematics, finite field arithmetic is arithmetic in a finite field (a field containing a finite number of elements) contrary to arithmetic in a field with an infinite number of elements, like the field of rational numbers. There are infinitely many different finite fields. Their number of elements is necessarily of the form pn where p is a prime number and n is a positive integer, and two finite fields of the same size are isomorphic.