Formal schemeIn mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Unlike an ordinary scheme, a formal scheme includes infinitesimal data that, in effect, points in a direction off of the scheme. For this reason, formal schemes frequently appear in topics such as deformation theory. But the concept is also used to prove a theorem such as the theorem on formal functions, which is used to deduce theorems of interest for usual schemes.
Attack modelIn cryptanalysis, attack models or attack types are a classification of cryptographic attacks specifying the kind of access a cryptanalyst has to a system under attack when attempting to "break" an encrypted message (also known as ciphertext) generated by the system. The greater the access the cryptanalyst has to the system, the more useful information they can get to utilize for breaking the cypher. In cryptography, a sending party uses a cipher to encrypt (transform) a secret plaintext into a ciphertext, which is sent over an insecure communication channel to the receiving party.
CryptanalysisCryptanalysis (from the Greek kryptós, "hidden", and analýein, "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown. In addition to mathematical analysis of cryptographic algorithms, cryptanalysis includes the study of side-channel attacks that do not target weaknesses in the cryptographic algorithms themselves, but instead exploit weaknesses in their implementation.
Man-in-the-middle attackIn cryptography and computer security, a man-in-the-middle attack is a cyberattack where the attacker secretly relays and possibly alters the communications between two parties who believe that they are directly communicating with each other, as the attacker has inserted themselves between the two parties. One example of a MITM attack is active eavesdropping, in which the attacker makes independent connections with the victims and relays messages between them to make them believe they are talking directly to each other over a private connection, when in fact the entire conversation is controlled by the attacker.
Cryptographic hash functionA cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with a fixed size of bits) that has special properties desirable for a cryptographic application: the probability of a particular -bit output result (hash value) for a random input string ("message") is (as for any good hash), so the hash value can be used as a representative of the message; finding an input string that matches a given hash value (a pre-image) is unfeasible, assuming all input str
Chosen-plaintext attackA chosen-plaintext attack (CPA) is an attack model for cryptanalysis which presumes that the attacker can obtain the ciphertexts for arbitrary plaintexts. The goal of the attack is to gain information that reduces the security of the encryption scheme. Modern ciphers aim to provide semantic security, also known as ciphertext indistinguishability under chosen-plaintext attack, and they are therefore, by design, generally immune to chosen-plaintext attacks if correctly implemented.
Derived schemeIn algebraic geometry, a derived scheme is a pair consisting of a topological space X and a sheaf either of simplicial commutative rings or of commutative ring spectra on X such that (1) the pair is a scheme and (2) is a quasi-coherent -module. The notion gives a homotopy-theoretic generalization of a scheme. A derived stack is a stacky generalization of a derived scheme. Over a field of characteristic zero, the theory is closely related to that of a differential graded scheme.
Ring learning with errorsIn post-quantum cryptography, ring learning with errors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms, such as NewHope, designed to protect against cryptanalysis by quantum computers and also to provide the basis for homomorphic encryption. Public-key cryptography relies on construction of mathematical problems that are believed to be hard to solve if no further information is available, but are easy to solve if some information used in the problem construction is known.
Public-key cryptographyPublic-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security.
Secure channelIn cryptography, a secure channel is a means of data transmission that is resistant to overhearing and tampering. A confidential channel is a means of data transmission that is resistant to overhearing, or eavesdropping (e.g., reading the content), but not necessarily resistant to tampering (i.e., manipulating the content). An authentic channel is a means of data transmission that is resistant to tampering but not necessarily resistant to overhearing.
