Cryptography in Constant Parallel Time by Benny Applebaum

Author:Benny Applebaum
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

We use a hybrid argument to show that such a distinguisher can be used to break the encryption hence deriving a contradiction.

5.2.4.2 Hybrid Encodings

From now on we fix n and let k=k(n). We construct a sequence of hybrid distributions that depend on x n , and mix “real” gates labels and “fake” ones, such that one endpoint corresponds to the simulated output (in which all the gates have “fake” labels) and the other endpoint corresponds to (in which all the gates have real labels). Hence, if the extreme hybrids can be efficiently distinguished then there must be two neighboring hybrids that can be efficiently distinguished.

The Hybrids

First, we order the gates of C n in topological order. That is, if the gate t uses the output of gate t′, then t′<t. Now, for every t=0,…,Γ(n), we define the hybrid algorithm that constructs “fake” labels for the first t gates and “real” labels for the rest of the gates: 1.For every wire i uniformly choose two 2k-bit strings and a random bit c i .

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