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Decisional Diffie–Hellman assumption
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==Definition== Consider a (multiplicative) [[cyclic group]] <math>G</math> of order <math>q</math>, and with [[Generating set of a group|generator]] <math>g</math>. The DDH assumption states that, given <math>g^a</math> and <math>g^b</math> for uniformly and independently chosen <math>a,b \in \mathbb{Z}_q</math>, the value <math>g^{ab}</math> "looks like" a random element in <math>G</math>. This intuitive notion can be formally stated by saying that the following two probability distributions are [[computationally indistinguishable]] (in the [[security parameter]], <math>n=\log(q)</math>): * <math>(g^a,g^b,g^{ab})</math>, where <math>a</math> and <math>b</math> are randomly and independently chosen from <math>\mathbb{Z}_q</math>. * <math>(g^a,g^b,g^c)</math>, where <math>a,b,c</math> are randomly and independently chosen from <math>\mathbb{Z}_q</math>. Triples of the first kind are often called '''DDH triplet''' or '''DDH tuples'''.
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