In cryptography, the hybrid argument is a proof technique used to show that two distributions are computationally indistinguishable.
Hybrid arguments had their origin in a papers by Andrew Yao in 1982 and Shafi Goldwasser and Silvio Micali in 1983.
[1] Formally, to show two distributions D1 and D2 are computationally indistinguishable, we can define a sequence of hybrid distributions D1 := H0, H1, ..., Ht =: D2 where t is polynomial in the security parameter n. Define the advantage of any probabilistic efficient (polynomial-bounded time) algorithm A as where the dollar symbol ($) denotes that we sample an element from the distribution at random.
By triangle inequality, it is clear that for any probabilistic polynomial time algorithm A, Thus there must exist some k s.t.
0 ≤ k < t(n) and Since t is polynomial-bounded, for any such algorithm A, if we can show that it has a negligible advantage function between distributions Hi and Hi+1 for every i, that is, then it immediately follows that its advantage to distinguish the distributions D1 = H0 and D2 = Ht must also be negligible.