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In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. The system provides an additional layer of security by asymmetrically encrypting keys previously used for symmetric message encryption. It was described by Taher Elgamal in 1985. ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems. The Digital Signature Algorithm (DSA) is a variant of the ElGamal signature scheme, which should not be confused with ElGamal encryption.
A cryptographically secure pseudo-random number generator (CSPRNG) or cryptographic pseudo-random number generator (CPRNG) is a pseudo-random number generator (PRNG) with properties that make it suitable for use in cryptography.
Articles related to cryptography include:
In cryptography, rubber-hose cryptanalysis is a euphemism for the extraction of cryptographic secrets from a person by coercion or torture—such as beating that person with a rubber hose, hence the name—in contrast to a mathematical or technical cryptanalytic attack.
In computer science, computational learning theory is a subfield of artificial intelligence devoted to studying the design and analysis of machine learning algorithms.
A cryptographic hash function is a special class of hash function that has certain properties which make it suitable for use in cryptography. It is a mathematical algorithm that maps data of arbitrary size to a bit string of a fixed size and is designed to be a one-way function, that is, a function which is infeasible to invert. The only way to recreate the input data from an ideal cryptographic hash function's output is to attempt a brute-force search of possible inputs to see if they produce a match, or use a rainbow table of matched hashes. Bruce Schneier has called one-way hash functions "the workhorses of modern cryptography". The input data is often called the message, and the output is often called the message digest or simply the digest.
In cryptography, a random oracle is an oracle that responds to every unique query with a (truly) random response chosen uniformly from its output domain. If a query is repeated it responds the same way every time that query is submitted.
Provable security refers to any type or level of security that can be proved. It is used in different ways by different fields.
The computational Diffie–Hellman (CDH) assumption is a computational hardness assumption about the Diffie-Hellman problem . The CDH assumption involves the problem of computing the discrete logarithm in cyclic groups. The CDH problem illustrates the attack of an eavesdropper in the Diffie-Hellman key exchange protocol to obtain the exchanged secret key.
The external Diffie–Hellman (XDH) assumption is a computational hardness assumption used in elliptic curve cryptography. The XDH assumption holds that there exist certain subgroups of elliptic curves which have useful properties for cryptography. Specifically, XDH implies the existence of two distinct groups with the following properties:
- The discrete logarithm problem (DLP), the computational Diffie–Hellman problem (CDH), and the computational co-Diffie–Hellman problem are all intractable in and .
- There exists an efficiently computable bilinear map (pairing) .
- The decisional Diffie–Hellman problem (DDH) is intractable in .
In computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently. It is not known how to prove (unconditional) hardness for essentially any useful problem. Instead, computer scientists rely on reductions to formally relate the hardness of a new or complicated problem to a computational hardness assumption about a problem that is better-understood.
Dan Boneh is a professor in applied cryptography and computer security at Stanford University.
The Decision Linear (DLIN) assumption is a computational hardness assumption used in elliptic curve cryptography. In particular, the DLIN assumption is useful in settings where the decisional Diffie–Hellman assumption does not hold. The Decision Linear assumption was introduced by Boneh, Boyen, and Shacham.
CEILIDH is a public key cryptosystem based on the discrete logarithm problem in algebraic torus. This idea was first introduced by Alice Silverberg and Karl Rubin in 2003; Silverberg named CEILIDH after her cat. The main advantage of the system is the reduced size of the keys for the same security over basic schemes.
Lattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or in the security proof. Lattice-based constructions are currently important candidates for post-quantum cryptography. Unlike more widely used and known public-key schemes such as the RSA, Diffie-Hellman or Elliptic-Curve cryptosystems, which are easily attacked by a quantum computer, some lattice-based constructions appear to be resistant to attack by both classical and quantum computers. Furthermore, many lattice-based constructions are known to be secure under the assumption that certain well-studied computational lattice problems cannot be solved efficiently.
Cryptography or cryptology is the practice and study of techniques for secure communication in the presence of third parties called adversaries. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages; various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, electrical engineering, communication science, and physics. Applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.
The decisional composite residuosity assumption (DCRA) is a mathematical assumption used in cryptography. In particular, the assumption is used in the proof of the Paillier cryptosystem.
Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution to the key exchange problem. The advantage of quantum cryptography lies in the fact that it allows the completion of various cryptographic tasks that are proven or conjectured to be impossible using only classical communication. For example, it is impossible to copy data encoded in a quantum state. If one attempts to read the encoded data, the quantum state will be changed. This could be used to detect eavesdropping in quantum key distribution.
In racing, Did Not Finish (DNF) denotes a participant who does not finish a given race, either because of a mechanical failure, injury, or involvement in an accident. The term is used in all forms of racing, including automotive racing, horse racing, cycling, track and distance running, and skiing, among other types of racing. Athletes try very hard to avoid receiving a DNF, and many associate it with a negative stigma.
In cryptography, security level is a measure of the strength that a cryptographic primitive — such as a cipher or hash function — achieves. Security level is usually expressed in "bits", where n-bit security means that the attacker would have to perform 2n operations to break it, but other methods have been proposed that more closely model the costs for an attacker. This allows for convenient comparison between algorithms and is useful when combining multiple primitives in a hybrid cryptosystem, so there is no clear weakest link. For example, AES-128 is designed to offer a 128-bit security level, which is considered roughly equivalent to 3072-bit RSA.
References
- ↑ Dan Boneh, Eu-Jin Goh, Kobbi Nissim: Evaluating 2-DNF Formulas on Ciphertexts. TCC 2005: 325–341
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