Multi-oracle Games Sample Clauses

Multi-oracle Games and an Existing Bound‌ Consider an adversary A interacting with multiple independent games {Gi = (Oi, Wi)}i∈I , (9) ∈ ∈ ∈ with as goal to win the disjunction of the Gi. Letting Xi denote the domain of oracle Oi and X the set of elements (i, x) such that x Xi, the game G = (O, W) that A plays can be defined with the single oracle O(i, x) = Oi(x), and by W where t W if the projection Πit of t onto the Oi-queries is in Wi for some i. If we know the security bounds for each Gi, then there is a simple way of bounding A’s advantage without computing it from scratch: for each i I construct an adversary Ai which runs A, plays game Gi, and simulates all the other games independently. The adversary Ai perfectly simulates A’s game precisely because game Gi is independent of all other games. Moreover, Xx wins if A does in game Gi. Then, taking a union bound over i, A’s advantage within q queries can be bounded by the sum of the advantages of the Ai for i ∈ I, or G,q Gi,q
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