Overview and Contributions Sample Clauses

Overview and Contributions. We set out to understand why there are seemingly no attacks matching the multi-key bounds established by the folklore result, and by formal proofs in cer- tain cases, against modes such as GCM. To do so, we systematically analyze the transition from games in which adversaries are given access to oracles rep- resenting a single, keyed algorithm, to games where adversaries are given access to multiple oracles representing different, independently keyed instances of an algorithm. The fact that the folklore result is the best generic reduction possible has already been established by Bellare, Boldyreva, and Micali [5], where they con- struct a public-key encryption scheme which necessarily has the μ-degradation. However, we take the informal guidance provided by such special cases a step further in Sect. 2, and point out that the multi-key setting is the natural one in which to consider weak keys, by illustrating how they can allow multi-key adver- saries to make better use of resources in comparison with single-key adversaries. In Sect. 3 we continue by distilling a sufficient condition under which adver- saries gain no advantage in the multi-key setting over the single-key setting. Informally, the condition states that it should always be better to attack an instance of an algorithm for which the adversary is given more information, as measured by the number of queries made to the instance. Note that this condi- tion is not satisfied for algorithms with weak keys: if the adversary knows that an instance uses a strong key, then it might be better for it to take its chances with an instance for which it has little information, but where it might get to attack a weak key. Although intuitively appealing, the condition that we extract can be difficult to use as a criterion in security analyses. Therefore in Sect. 4 we compare various methods for proving the absence of multi-key degradation, such as for the PRP- PRF switch and for Xxxxxx-Xxxxxx MACs [50]. Finally, we prove that GCM has security bounds that are independent of μ using our sufficient condition.
Sample 1
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