Title: Hellinger distance, distinguishability and adaptivity

Abstract: We discuss a new tool useful in certain cryptographic proofs called "sample distinguishability". In the sample distinguishability game, an information-theoretic distinguisher D has access to an indexed family of oracles, each of which is implemented by an independent random variable. Depending on which "world" D is in ("X world" or "Y world") each random variable in the family has a slightly different distribution. We discuss and prove upper bounds for D's advantage the two worlds when all distributions are known to D. A novel technical tool is the use of Hellinger distance and it turns out, interestingly, that measuring advantage in terms of Hellinger distance eliminates adaptivity. No technical background of any sort is required (including in cryptography), and all terms will be defined in the talk.