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Diffie–Hellman key exchange is a mathematical method of securely exchanging cryptographic keys over a public channel and was one of the first public-key protocols as conceived by Ralph Merkle and named after Whitfield Diffie and Martin Hellman. DH is one of the earliest practical examples of public key exchange implemented within the field of cryptography. Published in 1976 by Diffie and Hellman, this is the earliest publicly known work that proposed the idea of a private key and a corresponding public key.
Elliptic-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 to provide equivalent security.
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. 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.
In cryptography, the eXtended Sparse Linearization (XSL) attack is a method of cryptanalysis for block ciphers. The attack was first published in 2002 by researchers Nicolas Courtois and Josef Pieprzyk. It has caused some controversy as it was claimed to have the potential to break the Advanced Encryption Standard (AES) cipher, also known as Rijndael, faster than an exhaustive search. Since AES is already widely used in commerce and government for the transmission of secret information, finding a technique that can shorten the amount of time it takes to retrieve the secret message without having the key could have wide implications.
MQV (Menezes–Qu–Vanstone) is an authenticated protocol for key agreement based on the Diffie–Hellman scheme. Like other authenticated Diffie–Hellman schemes, MQV provides protection against an active attacker. The protocol can be modified to work in an arbitrary finite group, and, in particular, elliptic curve groups, where it is known as elliptic curve MQV (ECMQV).
Kleptography is the study of stealing information securely and subliminally. The term was introduced by Adam Young and Moti Yung in the Proceedings of Advances in Cryptology – Crypto '96. Kleptography is a subfield of cryptovirology and is a natural extension of the theory of subliminal channels that was pioneered by Gus Simmons while at Sandia National Laboratory. A kleptographic backdoor is synonymously referred to as an asymmetric backdoor. Kleptography encompasses secure and covert communications through cryptosystems and cryptographic protocols. This is reminiscent of, but not the same as steganography that studies covert communications through graphics, video, digital audio data, and so forth.
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.
In cryptography, a password-authenticated key agreement (PAK) method is an interactive method for two or more parties to establish cryptographic keys based on one or more party's knowledge of a password.
SPEKE is a cryptographic method for password-authenticated key agreement.
In cryptography, forward secrecy (FS), also known as perfect forward secrecy (PFS), is a feature of specific key-agreement protocols that gives assurances that session keys will not be compromised even if long-term secrets used in the session key exchange are compromised, limiting damage. For HTTPS, the long-term secret is typically the private key of the server. Forward secrecy protects past sessions against future compromises of keys or passwords. By generating a unique session key for every session a user initiates, the compromise of a single session key will not affect any data other than that exchanged in the specific session protected by that particular key. This by itself is not sufficient for forward secrecy which additionally requires that a long-term secret compromise does not affect the security of past session keys.
The Diffie–Hellman problem (DHP) is a mathematical problem first proposed by Whitfield Diffie and Martin Hellman in the context of cryptography and serves as the theoretical basis of the Diffie–Hellman key exchange and its derivatives. The motivation for this problem is that many security systems use one-way functions: mathematical operations that are fast to compute, but hard to reverse. For example, they enable encrypting a message, but reversing the encryption is difficult. If solving the DHP were easy, these systems would be easily broken.
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.
Distributed key generation (DKG) is a cryptographic process in which multiple parties contribute to the calculation of a shared public and private key set. Unlike most public key encryption models, distributed key generation does not rely on Trusted Third Parties. Instead, the participation of a threshold of honest parties determines whether a key pair can be computed successfully. Distributed key generation prevents single parties from having access to a private key. The involvement of many parties requires Distributed key generation to ensure secrecy in the presence of malicious contributions to the key calculation.
In cryptography, Curve25519 is an elliptic curve used in elliptic-curve cryptography (ECC) offering 128 bits of security and designed for use with the Elliptic-curve Diffie–Hellman (ECDH) key agreement scheme. It is one of the fastest curves in ECC, and is not covered by any known patents. The reference implementation is public domain software.
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 support important standards of post-quantum cryptography. Unlike more widely used and known public-key schemes such as the RSA, Diffie-Hellman or elliptic-curve cryptosystems — which could, theoretically, be defeated using Shor's algorithm on 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 considered 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 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. Core concepts related to information security are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.
Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms that are thought to be secure against a cryptanalytic attack by a quantum computer. The problem with popular algorithms currently used in the market 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. All of these problems could be easily solved on a sufficiently powerful quantum computer running Shor's algorithm or even faster and less demanding alternatives.
Supersingular isogeny Diffie–Hellman key exchange is an insecure proposal for a post-quantum cryptographic algorithm to establish a secret key between two parties over an untrusted communications channel. It is analogous to the Diffie–Hellman key exchange, but is based on walks in a supersingular isogeny graph and was designed to resist cryptanalytic attack by an adversary in possession of a quantum computer. Before it was broken, SIDH boasted one of the smallest key sizes of all post-quantum key exchanges; with compression, SIDH used 2688-bit public keys at a 128-bit quantum security level. SIDH also distinguishes itself from similar systems such as NTRU and Ring-LWE by supporting perfect forward secrecy, a property that prevents compromised long-term keys from compromising the confidentiality of old communication sessions. These properties seemed to make SIDH a natural candidate to replace Diffie–Hellman (DHE) and elliptic curve Diffie–Hellman (ECDHE), which are widely used in Internet communication. However, SIDH is vulnerable to a devastating key-recovery attack published in July 2022 and is therefore insecure. The attack does not require a quantum computer.
In cryptography, a public key exchange algorithm is a cryptographic algorithm which allows two parties to create and share a secret key, which they can use to encrypt messages between themselves. The ring learning with errors key exchange (RLWE-KEX) is one of a new class of public key exchange algorithms that are designed to be secure against an adversary that possesses a quantum computer. This is important because some public key algorithms in use today will be easily broken by a quantum computer if such computers are implemented. RLWE-KEX is one of a set of post-quantum cryptographic algorithms which are based on the difficulty of solving certain mathematical problems involving lattices. Unlike older lattice based cryptographic algorithms, the RLWE-KEX is provably reducible to a known hard problem in lattices.
References
- P. C. van Oorschot, M. J. Wiener. (May 1996). "On Diffie–Hellman key agreement with short exponents". Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques. Eurocrypt. Saragossa, Spain: Springer-Verlag. pp. 332–343. ISBN 3-540-61186-X.
- D. Jablon (October 1996). "Strong Password-Only Authenticated Key Exchange". ACM SIGCOMM Computer Communication Review. 26 (5): 5–26. doi:10.1145/242896.242897. S2CID 2870433.
- C.H. Lim and P.J. Lee. (1998). "A key recovery attack on discrete log-based schemes using a prime order subgroup". Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology. CRYPTO. Springer-Verlag. pp. 249–263. ISBN 3-540-63384-7.
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