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The '''computational Diffie–Hellman (CDH assumption)''' is the assumption that a certain [[computational problem]] within a [[cyclic group]] is hard.
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Consider a cyclic group ''G'' of order&nbsp;''q''. The CDH assumption states that, given
 
:<math>(g,g^a,g^b) \, </math>
 
for a randomly chosen generator ''g'' and random
 
:<math>a,b \in \{0, \ldots, q-1\},\,</math>
 
it is [[computationally intractable]] to compute the value
 
:<math>g^{ab}. \,</math>
 
The security of many [[cryptosystem]]s is based on the CDH assumption.  Also, the confidentiality of [[ElGamal encryption]] is equivalent to the CDH assumption (though the [[semantic security]] of the scheme is based on the [[decisional Diffie–Hellman assumption]]).
 
The CDH assumption is related to the [[discrete logarithm assumption]], which holds that computing the [[discrete logarithm]] of a value base a generator <math>g</math> is hard. If taking discrete logs in <math>{\mathbb G}</math> were easy, then the CDH assumption would be false: given
 
:<math>(g,g^a,g^b), \, </math>
 
one could efficiently compute <math>g^{ab}</math> in the following way:
* compute <math>a</math> by taking the discrete log of <math>g^a</math> to base <math>g</math>;
* compute <math>g^{ab}</math> by exponentiation: <math>g^{ab} = (g^b)^a</math>;
 
It is an open problem to determine whether the discrete log assumption is equivalent to CDH, though in certain special cases this can be shown to be the case.
 
The CDH assumption is also related to the [[decisional Diffie–Hellman assumption]] (DDH), which holds that it is hard to distinguish tuples of the form <math>(g,g^a,g^b,g^{ab})</math> from random tuples. If computing <math>g^{ab}</math> from <math>(g,g^a,g^b)</math> were easy, then one could detect DDH tuples trivially. It is believed that CDH is a '''weaker''' assumption than DDH: there are groups for which detecting DDH tuples is easy, but solving CDH problems is believed to be hard.
 
==See also==
* [[Diffie–Hellman problem]]
* [[Diffie–Hellman key exchange]]
 
==References==
#Variations of the Diffie–Hellman Problem ([http://www.i2r.a-star.edu.sg/icsd/publications/Baofeng_2003_Variations%20of%20Diffie%20Hellman%20problems.pdf pdf file])
#Towards the Equivalence of Breaking the Diffie–Hellman Protocol and Computing Discrete Logarithms ([http://dsns.csie.nctu.edu.tw/research/crypto/HTML/PDF/C94/271.PDF pdf file])
 
{{DEFAULTSORT:Computational Diffie-Hellman assumption}}
[[Category:Computational hardness assumptions]]

Revision as of 19:22, 26 February 2014

Welcome to Propwise.sg, a Singapore property blog dedicated to serving to you perceive the actual estate market and make better choices – minus the hype and misinformation. A person's video rant on about Singapore Chinese language ladies has attracted a whole lot of consideration. For HDB flats, HDB shophouse and government condominiums, eligibility is subjected to the Housing And Improvement Board (HDB) CNBC produced a slideshow on The World's Hottest Real Property Markets and I used to be not shocked Singapore made the top 10 checklist.

The new tax obligation will hit as a result of the Mortgage Forgiveness Debt Relief Act expires on the end of the year. The 2007 law was handed to save lots of struggling owners from getting whacked twice, first by the sagging housing market and second by the Inner Income Service. Its expiration could push more folks to stay in houses price less than their mortgages, slowing the housing market's recovery. We've already seen conditions where people who find themselves considering new property launch singapore promoting their dwelling - getting it able to sell - should not listing their houses on the market until this challenge is resolved," mentioned Goold. "The longer it drags out and the further into 2013, the more chilling results the failure to extend the relief may have on the housing recovery."

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