feat(Crypto): prove hybrid arguments with polynomially many hops - #1070
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Adds `Cslib.Crypto.Game.Hybrid`. The advantage between the endpoints of a chain of games is at most the sum of the adjacent advantages, so polynomially many hops with one common negligible bound per adversary give negligible total advantage (`Secure.hybrid`). Choosing the hop uniformly at random telescopes the signed gaps (`advantage_hybrid_average`). This gives one reduction for every security parameter, whose loss is the number of hops, without selecting a length-dependent best hop ([AroraBarak09] §9.3). `Secure.of_reduction_with_loss` lets a reduction lose a polynomial factor and incur a negligible error.
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Adds
Cslib.Crypto.Game.Hybrid. Bounds endpoint advantage by the sum of adjacent advantages and proves negligible total advantage for polynomially many hops sharing one negligible bound per adversary (Secure.hybrid).Proves exact signed-gap and advantage identities for uniformly sampled adjacent hybrids, with unused indices rejecting. The averaging loss is the sampling capacity, which may exceed the number of hops.
Secure.of_reduction_with_losstransfers security through an admissibility-preserving reduction with polynomial loss and negligible additive error; both bounds may depend on the adversary.Reference: Arora and Barak, Computational Complexity: A Modern Approach, §9.3.
Depends on #1069.
Composed with Claude Code; reviewed and restacked with Codex.