Information-Theoretic Indistinguishability via the Chi-Squared Method

Proving tight bounds on information-theoretic indistinguishability is a central problem in symmetric cryptography. This paper introduces a new method for information-theoretic indistinguishability proofs, called “the chi-squared method”. At its core, the method requires upper-bounds on the so-called \(\chi ^2\) divergence (due to Neyman and Pearson) between the output distributions of two systems being queries. The method morally resembles, yet also considerably simplifies, a previous approach proposed by Bellare and Impagliazzo (ePrint, 1999), while at the same time increasing its expressiveness and delivering tighter bounds.

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