# Question on definition of semantic security: why "probability ensemble"?

Hi!
I was often stumbling over this question and could not get a clear
explanation, so maybe someone here would be able to help me.

Why does the definition of semantic security use a notion of
"probability ensemble" (e.g. in Goldreich's "Foundations of
Cryptography II")? According to this definition an encryption scheme is
semantically secure if for any PPT algorithm A there exists a PPT
algorithm A' such that for every probability ensemble {X_n}

Pr[A(E_k(X_n))=1] < Pr[A'(lengthof(X_n))=1] + 1/poly(n)

Why not to say "for any plaintext x_n \in {0,1}^n" instead of
"probability ensemble"?

Sergei

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