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Diffie—Hellman key exchange DH volume de negociation bitcoin par echange 1] is a method of securely exchanging cryptographic keys over a public channel and was one of the first public-key protocols as originally conceptualized by Ralph Merkle and named after Whitfield Diffie and Martin Hellman. Traditionally, secure encrypted communication between two parties required that they first exchange keys by some secure physical channel, such as paper key lists transported by a trusted courier.
The Diffie—Hellman key exchange method allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure channel. This key can then be used to encrypt subsequent communications using a symmetric key cipher. Diffie—Hellman is used to secure a variety of Internet services. However, research published in October suggests that the parameters in use for many DH Internet applications at that time are not strong enough to prevent compromise by very well-funded attackers, such as the security services of large governments.
The scheme was first published by Whitfield Diffie and Martin Hellman in[2] but in it was revealed that James H. Ellis[4] Clifford Cocks and Volume de negociation bitcoin par echange J. Williamson of GCHQthe British signals intelligence agency, had previously, in[5] shown how public-key cryptography could be achieved. Although Diffie—Hellman key agreement itself is a non-authenticated key-agreement protocolit provides the basis for a variety of authenticated protocols, and is used to provide forward secrecy in Transport Layer Security 's ephemeral modes referred to as EDH or DHE depending on the cipher suite.
The method was followed shortly afterwards by RSAan implementation of public-key cryptography using asymmetric algorithms. Patent 4, fromis now expired and describes the now-public domain algorithm. It credits Hellman, Diffie, and Merkle as inventors. InHellman suggested the algorithm be called Diffie—Hellman—Merkle volume de negociation bitcoin par echange exchange in recognition of Ralph Merkle 's contribution to the invention of public-key cryptography Hellman,writing:.
Diffie—Hellman Key Exchange establishes a shared secret between two parties that can be used for secret communication for exchanging data over a public network. The following conceptual diagram illustrates the general idea of the key exchange by using colors instead of very large numbers. The process begins by having the two parties, Alice and Bobagree on an arbitrary starting color that does not need to be kept secret but should be different every time [8] ; in this example the color is yellow.
Each of them selects a secret color that they keep to themselves. In this case, orange and blue-green. The crucial part of the process is that Alice and Bob now mix their secret color together with their mutually shared color, resulting in orange-tan and light-blue mixtures respectively, then publicly exchange the two mixed colors. Finally, each of the two mix together the color they received from the partner with their own private color.
The result is a final color mixture yellow-brown that is identical to the partner's color mixture. If a third party listened to the exchange, it would be computationally difficult for them to determine the secret colors. In fact, when using large numbers rather than colors, this action is computationally expensive for modern supercomputers to do in a reasonable amount of time.
The simplest and the original implementation of the protocol uses the multiplicative group of integers modulo pwhere p is primeand g is a primitive root modulo p.
These two values are chosen in this way to ensure that the resulting shared secret can take on any value from 1 to p —1. Here is an example of the protocol, with non-secret values in blueand secret values in red. All the other values — pgg a mod pand g b mod p — are sent in the clear. Once Alice and Bob compute the shared secret they can use it as an encryption key, known only to them, for sending messages across the same open communications channel.
Of course, much larger values of aband p would be needed to make this example secure, since there are only 23 possible results of n mod However, if p is a prime of at least digits, then even the fastest modern computers cannot find a given only gp and g a mod p.
Such a problem is called the discrete logarithm problem. Note that g need not be large at all, and in practice is usually a small integer like 2, 3, The chart below depicts who knows what, again with non-secret values in blueand secret values in red. Here Eve is an eavesdropper —she watches what is sent between Alice and Bob, but she does not alter the contents of their communications. Volume de negociation bitcoin par echange s is the shared secret key and it is known to both Alice and Bob, but not to Eve.
It should be difficult for Alice to solve for Bob's private key or for Bob to solve for Alice's private key. Another demonstration of Diffie—Hellman also using numbers too small for practical use is given here. Here is a more general description of the protocol: Both Alice and Bob are now in possession of the group element g abwhich can serve as the shared secret key. The group G satisfies the requisite condition for secure communication if there is volume de negociation bitcoin par echange an efficient algorithm for determining g ab given gg aand g b.
For example, the elliptic curve Diffie—Hellman protocol is variant that uses elliptic curves instead of the multiplicative group of integers modulo p. Variants using hyperelliptic curves have also been proposed. The supersingular isogeny key exchange is a Diffie—Hellman variant that has been designed to be secure against quantum computers. Diffie—Hellman key agreement is not limited to negotiating a key shared by only two participants.
Any number of users can take part in an agreement by performing iterations of the agreement protocol and exchanging intermediate data which does not itself need to be kept secret. For example, Alice, Bob, and Carol could participate in a Diffie—Hellman agreement as follows, volume de negociation bitcoin par echange all operations taken to be modulo p:. An eavesdropper has been able to see g ag bg cg abg acand g bcbut cannot use any combination of these to efficiently reproduce g abc.
These principles leave open various options for choosing in which order participants contribute to keys. The simplest and most obvious volume de negociation bitcoin par echange is to arrange volume de negociation bitcoin par echange N participants in a circle and have N keys rotate around the circle, until eventually every key has been contributed to by all N participants ending with its owner and volume de negociation bitcoin par echange participant has contributed to N keys ending with their own.
However, this requires that every participant perform N modular exponentiations. Once this operation has been completed all participants will possess the secret g abcdefghbut each participant will have performed only four modular exponentiations, rather than the eight implied by a simple circular arrangement. The protocol is considered secure against eavesdroppers if G and g are chosen properly. In particular, volume de negociation bitcoin par echange order of the group G must be large, particularly if the same group is used for large amounts of traffic.
The eavesdropper " Eve " has to solve the Diffie—Hellman problem to obtain g ab. This is currently considered difficult for groups whose order is large enough. An efficient algorithm to solve the discrete logarithm problem would make it easy to compute a or b and solve the Diffie—Hellman problem, making this and many other public key cryptosystems insecure. Fields of volume de negociation bitcoin par echange characteristic may be less secure.
The order of G should have a large prime factor to prevent use of the Pohlig—Hellman algorithm to obtain a or b. A protocol using such a choice is for example IKEv2. Because of the random self-reducibility of the discrete logarithm problem a small g is equally secure as any other generator of the same group.
If Alice and Bob use random number generators whose outputs are not completely random and can be predicted to some extent, then Eve's task is much easier. In the original description, the Diffie—Hellman exchange by itself does not provide authentication of the communicating parties and is thus vulnerable to a man-in-the-middle attack.
Mallory an active attacker executing the man-in-the-middle attack may establish two distinct key exchanges, one with Alice and the other with Bob, effectively masquerading as Alice to Bob, and vice versa, allowing her to decrypt, then re-encrypt, the messages passed between them. Note that Mallory must continue to be in the middle, transferring messages every time Alice and Bob communicate. If she is ever absent, her previous presence is then revealed to Alice and Bob.
They will know that all of their private conversations had been intercepted and decoded by someone in the channel.
A method to authenticate the communicating parties to each other is generally needed to prevent this type of attack. Variants of Diffie—Hellman, such as STS protocolmay be used instead to avoid these types of attacks. The number field sieve algorithm, which is generally the most effective in solving the discrete logarithm problemconsists of four computational steps.
The first three steps only depend on the order of the group G, not on the specific number whose finite log is desired. The Logjam attack used this vulnerability to compromise a variety of Internet services that allowed the use of groups whose order was a bit prime number, so called export grade. The volume de negociation bitcoin par echange needed several thousand CPU cores for a week to precompute data for a single bit prime. Once that was done, individual logarithms could be solved in about a minute using two core Intel Xeon CPUs.
The Logjam authors speculate that precomputation against widely reused bit DH primes is behind claims in leaked NSA documents that NSA is able to break much of current cryptography. To avoid these vulnerabilities, authors recommend use of elliptic curve cryptographyfor which no similar attack is known.
They estimate that the pre-computation required for a bit prime is 10 9 more difficult than for bit primes. Public key encryption schemes based on the Diffie—Hellman key exchange have been proposed. The first such scheme is the ElGamal encryption. A more modern variant is the Integrated Encryption Scheme. Protocols that achieve forward secrecy generate new key pairs for each session and discard them at the end of the session.
The Diffie—Hellman key exchange is a frequent choice for such protocols, because of its fast key generation. When Alice and Bob share a password, they may use a password-authenticated key agreement PK form of Diffie—Hellman to prevent man-in-the-middle attacks.
One simple scheme is to compare the hash of s concatenated with the password calculated independently on both ends of channel. A feature of these schemes is that an attacker can only test one specific password on each iteration with the other party, and so the system provides good security with relatively weak passwords.
An example of such a protocol is the Secure Remote Password Protocol. It is also possible volume de negociation bitcoin par echange use Diffie—Hellman as part of a public key infrastructureallowing Bob to encrypt a message so that only Volume de negociation bitcoin par echange will be able to decrypt it, with no prior communication between them other than Bob having trusted knowledge of Alice's public key. Only Alice can determine the symmetric key and hence decrypt the message because only she has a the private key.
A pre-shared public key also prevents man-in-the-middle attacks. In practice, Diffie—Hellman is not used in this way, with Volume de negociation bitcoin par echange being the dominant public key algorithm. This is largely for historical and commercial reasons [ citation needed ]namely that RSA Security created a certificate authority for key signing that became Verisign.
Diffie—Hellman cannot be used to sign certificates. From Wikipedia, the free encyclopedia. This article has multiple issues. Please help improve it or discuss these issues on the talk volume de negociation bitcoin par echange.
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