Elliptic-curve cryptographyElliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme.
Discrete logarithmIn mathematics, for given real numbers a and b, the logarithm logb a is a number x such that bx = a. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm logb a is an integer k such that bk = a. In number theory, the more commonly used term is index: we can write x = indr a (mod m) (read "the index of a to the base r modulo m") for rx ≡ a (mod m) if r is a primitive root of m and gcd(a,m) = 1. Discrete logarithms are quickly computable in a few special cases.
Key sizeIn cryptography, key size, key length, or key space refer to the number of bits in a key used by a cryptographic algorithm (such as a cipher). Key length defines the upper-bound on an algorithm's security (i.e. a logarithmic measure of the fastest known attack against an algorithm), because the security of all algorithms can be violated by brute-force attacks. Ideally, the lower-bound on an algorithm's security is by design equal to the key length (that is, the algorithm's design does not detract from the degree of security inherent in the key length).
Advanced Encryption StandardThe Advanced Encryption Standard (AES), also known by its original name Rijndael (ˈrɛindaːl), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001. AES is a variant of the Rijndael block cipher developed by two Belgian cryptographers, Joan Daemen and Vincent Rijmen, who submitted a proposal to NIST during the AES selection process. Rijndael is a family of ciphers with different key and block sizes.
Key (cryptography)A key in cryptography is a piece of information, usually a string of numbers or letters that are stored in a file, which, when processed through a cryptographic algorithm, can encode or decode cryptographic data. Based on the used method, the key can be different sizes and varieties, but in all cases, the strength of the encryption relies on the security of the key being maintained. A key's security strength is dependent on its algorithm, the size of the key, the generation of the key, and the process of key exchange.
Traffic analysisTraffic analysis is the process of intercepting and examining messages in order to deduce information from patterns in communication. It can be performed even when the messages are encrypted. In general, the greater the number of messages observed, the greater information be inferred. Traffic analysis can be performed in the context of military intelligence, counter-intelligence, or pattern-of-life analysis, and is also a concern in computer security. Traffic analysis tasks may be supported by dedicated computer software programs.
Post-quantum cryptographyIn cryptography, post-quantum cryptography (PQC) (sometimes referred to as quantum-proof, quantum-safe or quantum-resistant) refers to cryptographic algorithms (usually public-key algorithms) that are thought to be secure against a cryptanalytic attack by a quantum computer. The problem with currently popular algorithms is that their security relies on one of three hard mathematical problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve discrete logarithm problem.
Automorphism groupIn mathematics, the automorphism group of an object X is the group consisting of automorphisms of X under composition of morphisms. For example, if X is a finite-dimensional vector space, then the automorphism group of X is the group of invertible linear transformations from X to itself (the general linear group of X). If instead X is a group, then its automorphism group is the group consisting of all group automorphisms of X. Especially in geometric contexts, an automorphism group is also called a symmetry group.
CryptographyCryptography, or cryptology (from κρυπτός "hidden, secret"; and γράφειν graphein, "to write", or -λογία -logia, "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others.
Elliptic curveIn mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over a field K and describes points in K^2, the Cartesian product of K with itself. If the field's characteristic is different from 2 and 3, then the curve can be described as a plane algebraic curve which consists of solutions (x, y) for: for some coefficients a and b in K. The curve is required to be non-singular, which means that the curve has no cusps or self-intersections.
