feat(Crypto): add security games - #1069
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Adds `Cslib.Crypto.Game`. A `Game` is a `PMF Bool`, the distribution of a Boolean experiment, and `advantage` is the absolute difference of acceptance probabilities ([BonehShoup2023] §3.1). It satisfies the triangle inequality used in game hopping. `Game.Secure real ideal Admissible` says that every admissible adversary has negligible advantage, with admissibility checked before the security parameter is chosen. `Game.SecureWithError` asks instead for a common concrete bound at each parameter. Both come with monotonicity, symmetry, transitivity, and reduction lemmas. Stating these once lets finite primitives such as the PRG games and computational definitions over infinite sample spaces share one advantage convention.
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samschles/crypto-pr-03-statistical-distance-tsum
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Adds
Cslib.Crypto.Game, representing Boolean experiments asPMF Bool. Distinguishing advantage is the absolute difference of acceptance probabilities, following Boneh and Shoup, §3.1.Game.Securerequires negligible advantage for each admissible adversary, with admissibility applied to the whole adversary before choosing a security parameter.Game.SecureWithErrorgives a common concrete bound for all admissible adversaries.Includes symmetry and game-hopping lemmas, restriction of admissible adversaries, asymptotic security reductions, and conversion from a negligible concrete bound to asymptotic security. These definitions let PRG games and experiments over infinite sample spaces share one security API.
Depends on #1065.
Composed with Claude Code; reviewed and restacked with Codex.