Reference Work Entry

Encyclopedia of Cryptography and Security

pp 240-244

Computational Diffie-Hellman Problem

  • Igor ShparlinskiAffiliated withDepartment of Computing Faculty of Science, Macquarie University


CDH; DHP; Diffie-Hellman problem

Related Concepts

Computational Complexity; Decisional Diffie-Hellman Problem; Diffie–Hellman Key Agreement; Discrete Logarithm Problem; Public Key Cryptography


Let G be a cyclic group with generatorg and let \({g}^{x},{g}^{y} \in G\). The computational Diffie-Hellman problem is to compute gxy.


In their pioneering paper, Diffie and Hellman [10] proposed an elegant, reliable, and efficient way to establish a common key between two communicating parties. In the most general setting their idea can be described as follows (see Diffie-Hellman key agreement for further discussion). Given a cyclic groupG and agenerator gof G,two communicating parties Alice and Bob execute the following protocol:

  • Alice selects secret x, Bob selects secret y

  • Alice publishes X = gx, Bob publishes Y = gy

  • Alice computes K = Yx, Bob computes K = Xy

Therefore, at the end of the protocol the values X = gx and Y = g ...

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