Diffie-Hellman

(cryptography)

A public-key encryption key exchange algorithm.

FAQ.

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Diffie-Hellman

A cryptographic key exchange method developed by Whitfield Diffie and Martin Hellman in 1976. Also known as the "Diffie-Hellman-Merkle" method and "exponential key agreement." Diffie-Hellman enables parties at both ends to derive a shared, secret key from a common starting point without the key ever being transmitted from one side to the other.

Although Diffie-Hellman is an asymmetric algorithm, it does not use public and private keys like the popular RSA method. Its logarithms and modular arithmetic are complicated mathematics; however, the example below is simplified to explain the concept. The numbers used are minuscule by comparison to those used in a real exchange. See elliptic curve cryptography, RSA and key management.

Very Clever Math

Both sides use a public common number, and each side uses a different random number as a power to raise the common number. The results are then sent to each other. The receiving party raises the received number to the same random power they used before, and the results wind up the same on both sides.

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References in periodicals archive

Elliptic curve Diffie-Hellman is an is an obscure key conformity protocol that permits two clients, each having an elliptic bend public-private key combine off, to create a mutual undisclosed over an uncertain channel.

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Bernstein, "Curve25519: New Diffie-Hellman Speed Records", in Public Key Cryptography (PKC 2006), Lecture Notes in Computer Science, vol.

Anomalous Behaviour of Cryptographic Elliptic Curves over Finite Field

An adversary who intercepts R, z, s, T, g, h, and C between the reader and the tag and attempts to obtain the tag ID cannot get the session key KTR, because this is computationally infeasible under the Diffie-Hellman problem and the elliptic curve discrete logarithm problem (ECDLP).

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For commonly used 1024-bit keys, it would take about a year and cost a "few hundred million dollars" to crack just one of the extremely large prime numbers that form the starting point of a Diffie-Hellman negotiation.

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Elliptic Curve Computational Diffie-Hellman Problem (ECCDHP): Given G and two point xG, yG, computation of xyG is hard, where x, y [member of] [Z.sub.p.sup.*] and are randomly chosen and are smaller than n.

On Security Analysis of Recent Password Authentication and Key Agreement Schemes Based on Elliptic Curve Cryptography

Assuming the hardness of computational Diffie-Hellman problem over groups in bilinear maps, the proposed CLAS scheme is proven secure in random oracle model, Bellare and Rogaway (1993).

An efficient certificateless aggregate signature scheme for vehicular ad-hoc networks

(2.) Rouse, M., "Diffie-Hellman key exchange (exponential key exchange)," TechTarget, August 2007.

The importance of trapdoor functions