feat(Crypto): relate security games to statistical distance - #1072
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Adds `Cslib.Crypto.Game.Statistical`. For Boolean experiments, advantage equals statistical distance, so no randomized test distinguishes two distributions better than their statistical distance, on finite or infinite sample types. `StatisticallyIndistinguishable` says that two ensembles have negligible statistical distance; it is an equivalence, is closed under `bind` and `map`, and implies security against any class of tests. `Cslib.Crypto.Primitives.PRG.Statistical` applies this to the PRG games: a generator whose output is statistically close to the ideal distribution is secure, concretely and asymptotically.
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Connects Boolean security games to statistical distance:
Game.advantage_eq_distidentifies the two quantities, and the existing PMF contraction lemmas bound every randomized test’s advantage.StatisticallyIndistinguishableexpresses negligible statistical distance between parameter-indexed ensembles, following Boneh and Shoup, §3.11. It is reflexive, symmetric, and transitive, and is preserved by applying the same randomized or deterministic postprocessing to both ensembles. The statements do not require finite ambient types or finite supports.Cslib.Crypto.Primitives.PRG.Statisticalderives concrete and asymptotic PRG security from statistical-distance bounds, for explicit seed and ideal distributions and any chosen class of adversaries.Depends on #1071.
Composed with Claude Code; reviewed and restacked with Codex.