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.
NP (complexity)In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. NP is the set of decision problems solvable in polynomial time by a nondeterministic Turing machine.
Feistel cipherIn cryptography, a Feistel cipher (also known as Luby–Rackoff block cipher) is a symmetric structure used in the construction of block ciphers, named after the German-born physicist and cryptographer Horst Feistel, who did pioneering research while working for IBM; it is also commonly known as a Feistel network. A large proportion of block ciphers use the scheme, including the US Data Encryption Standard, the Soviet/Russian GOST and the more recent Blowfish and Twofish ciphers.
Key stretchingIn cryptography, key stretching techniques are used to make a possibly weak key, typically a password or passphrase, more secure against a brute-force attack by increasing the resources (time and possibly space) it takes to test each possible key. Passwords or passphrases created by humans are often short or predictable enough to allow password cracking, and key stretching is intended to make such attacks more difficult by complicating a basic step of trying a single password candidate.
Computational complexity theoryIn theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.
Chosen-ciphertext attackA chosen-ciphertext attack (CCA) is an attack model for cryptanalysis where the cryptanalyst can gather information by obtaining the decryptions of chosen ciphertexts. From these pieces of information the adversary can attempt to recover the hidden secret key used for decryption. For formal definitions of security against chosen-ciphertext attacks, see for example: Michael Luby and Mihir Bellare et al. A number of otherwise secure schemes can be defeated under chosen-ciphertext attack.
Cubic equationIn algebra, a cubic equation in one variable is an equation of the form in which a is nonzero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation can be found by the following means: algebraically: more precisely, they can be expressed by a cubic formula involving the four coefficients, the four basic arithmetic operations, square roots and cube roots.
Stream cipherA stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream (keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystream, to give a digit of the ciphertext stream. Since encryption of each digit is dependent on the current state of the cipher, it is also known as state cipher. In practice, a digit is typically a bit and the combining operation is an exclusive-or (XOR).
Preimage attackIn cryptography, a preimage attack on cryptographic hash functions tries to find a message that has a specific hash value. A cryptographic hash function should resist attacks on its (set of possible inputs). In the context of attack, there are two types of preimage resistance: preimage resistance: for essentially all pre-specified outputs, it is computationally infeasible to find any input that hashes to that output; i.e., given , it is difficult to find an such that () = .
Symmetric-key algorithmSymmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both the encryption of plaintext and the decryption of ciphertext. The keys may be identical, or there may be a simple transformation to go between the two keys. The keys, in practice, represent a shared secret between two or more parties that can be used to maintain a private information link. The requirement that both parties have access to the secret key is one of the main drawbacks of symmetric-key encryption, in comparison to public-key encryption (also known as asymmetric-key encryption).
