Mathematical proofA mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation".
Mathematical inductionMathematical induction is a method for proving that a statement is true for every natural number , that is, that the infinitely many cases all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step). A proof by induction consists of two cases.
Computer-assisted proofA computer-assisted proof is a mathematical proof that has been at least partially generated by computer. Most computer-aided proofs to date have been implementations of large proofs-by-exhaustion of a mathematical theorem. The idea is to use a computer program to perform lengthy computations, and to provide a proof that the result of these computations implies the given theorem. In 1976, the four color theorem was the first major theorem to be verified using a computer program.
Proofs and RefutationsProofs and Refutations: The Logic of Mathematical Discovery is a 1976 book by philosopher Imre Lakatos expounding his view of the progress of mathematics. The book is written as a series of Socratic dialogues involving a group of students who debate the proof of the Euler characteristic defined for the polyhedron. A central theme is that definitions are not carved in stone, but often have to be patched up in the light of later insights, in particular failed proofs. This gives mathematics a somewhat experimental flavour.
Proof theoryProof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.
HTTPSHypertext Transfer Protocol Secure (HTTPS) is an extension of the Hypertext Transfer Protocol (HTTP). It uses encryption for secure communication over a computer network, and is widely used on the Internet. In HTTPS, the communication protocol is encrypted using Transport Layer Security (TLS) or, formerly, Secure Sockets Layer (SSL). The protocol is therefore also referred to as HTTP over TLS, or HTTP over SSL. The principal motivations for HTTPS are authentication of the accessed website and protection of the privacy and integrity of the exchanged data while it is in transit.
CryptocurrencyA cryptocurrency, crypto-currency, or crypto is a digital currency designed to work as a medium of exchange through a computer network that is not reliant on any central authority, such as a government or bank, to uphold or maintain it. It is a decentralized system for verifying that the parties to a transaction have the money they claim to have, eliminating the need for traditional intermediaries, such as banks, when funds are being transferred between two entities.
Cryptocurrency walletA cryptocurrency wallet is a device, physical medium, program or a service which stores the public and/or private keys for cryptocurrency transactions. In addition to this basic function of storing the keys, a cryptocurrency wallet more often offers the functionality of encrypting and/or signing information. Signing can for example result in executing a smart contract, a cryptocurrency transaction (see "bitcoin transaction" image), identification or legally signing a 'document' (see "application form" image).
Communication protocolA communication protocol is a system of rules that allows two or more entities of a communications system to transmit information via any variation of a physical quantity. The protocol defines the rules, syntax, semantics, and synchronization of communication and possible error recovery methods. Protocols may be implemented by hardware, software, or a combination of both. Communicating systems use well-defined formats for exchanging various messages.
Cryptocurrency exchangeA cryptocurrency exchange, or a digital currency exchange (DCE), is a business that allows customers to trade cryptocurrencies or digital currencies for other assets, such as conventional fiat money or other digital currencies. Exchanges may accept credit card payments, wire transfers or other forms of payment in exchange for digital currencies or cryptocurrencies. A cryptocurrency exchange can be a market maker that typically takes the bid–ask spreads as a transaction commission for its service or, as a matching platform, simply charges fees.
Authentication protocolAn authentication protocol is a type of computer communications protocol or cryptographic protocol specifically designed for transfer of authentication data between two entities. It allows the receiving entity to authenticate the connecting entity (e.g. Client connecting to a Server) as well as authenticate itself to the connecting entity (Server to a client) by declaring the type of information needed for authentication as well as syntax. It is the most important layer of protection needed for secure communication within computer networks.
Transport Layer SecurityTransport Layer Security (TLS) is a cryptographic protocol designed to provide communications security over a computer network. The protocol is widely used in applications such as email, instant messaging, and voice over IP, but its use in securing HTTPS remains the most publicly visible. The TLS protocol aims primarily to provide security, including privacy (confidentiality), integrity, and authenticity through the use of cryptography, such as the use of certificates, between two or more communicating computer applications.
Information securityInformation security, sometimes shortened to InfoSec, is the practice of protecting information by mitigating information risks. It is part of information risk management. It typically involves preventing or reducing the probability of unauthorized or inappropriate access to data or the unlawful use, disclosure, disruption, deletion, corruption, modification, inspection, recording, or devaluation of information. It also involves actions intended to reduce the adverse impacts of such incidents.
HTTPThe Hypertext Transfer Protocol (HTTP) is an application layer protocol in the Internet protocol suite model for distributed, collaborative, hypermedia information systems. HTTP is the foundation of data communication for the World Wide Web, where hypertext documents include hyperlinks to other resources that the user can easily access, for example by a mouse click or by tapping the screen in a web browser. Development of HTTP was initiated by Tim Berners-Lee at CERN in 1989 and summarized in a simple document describing the behavior of a client and a server using the first HTTP version, named 0.
Information security auditAn information security audit is an audit of the level of information security in an organization. It is an independent review and examination of system records, activities, and related documents. These audits are intended to improve the level of information security, avoid improper information security designs, and optimize the efficiency of the security safeguards and security processes. Within the broad scope of auditing information security there are multiple types of audits, multiple objectives for different audits, etc.
Undefined behaviorIn computer programming, undefined behavior (UB) is the result of executing a program whose behavior is prescribed to be unpredictable, in the language specification to which the computer code adheres. This is different from unspecified behavior, for which the language specification does not prescribe a result, and implementation-defined behavior that defers to the documentation of another component of the platform (such as the ABI or the translator documentation).
Formal verificationIn the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics. Formal verification can be helpful in proving the correctness of systems such as: cryptographic protocols, combinational circuits, digital circuits with internal memory, and software expressed as source code.
Source-to-source compilerA source-to-source translator, source-to-source compiler (S2S compiler), transcompiler, or transpiler is a type of translator that takes the source code of a program written in a programming language as its input and produces an equivalent source code in the same or a different programming language. A source-to-source translator converts between programming languages that operate at approximately the same level of abstraction, while a traditional compiler translates from a higher level programming language to a lower level programming language.
Security engineeringSecurity engineering is the process of incorporating security controls into an information system so that the controls become an integral part of the system’s operational capabilities. It is similar to other systems engineering activities in that its primary motivation is to support the delivery of engineering solutions that satisfy pre-defined functional and user requirements, but it has the added dimension of preventing misuse and malicious behavior. Those constraints and restrictions are often asserted as a security policy.
Null pointerIn computing, a null pointer or null reference is a value saved for indicating that the pointer or reference does not refer to a valid object. Programs routinely use null pointers to represent conditions such as the end of a list of unknown length or the failure to perform some action; this use of null pointers can be compared to nullable types and to the Nothing value in an option type. A null pointer should not be confused with an uninitialized pointer: a null pointer is guaranteed to compare unequal to any pointer that points to a valid object.
