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12.5. MACs are, in principle, also vulnerable against collision attacks. We discuss the issue in the following. 1. Assume Oscar found a collision between two

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12.5. MACs are, in principle, also vulnerable against collision attacks. We discuss the issue in the following. 1. Assume Oscar found a collision between two messages, i.e., MACE(xi) MACEx2) Show a simple protocol with an attack that is based on a collision. 2. Even though the birthday paradox can still be used for constructing collisions, why is it in a practical setting much harder to construct them for MACs than for hash functions? Since this is the case: what security is provided by a MAC with 80-bit output compared to a hash function with 80-bit output? 12.5. MACs are, in principle, also vulnerable against collision attacks. We discuss the issue in the following. 1. Assume Oscar found a collision between two messages, i.e., MACE(xi) MACEx2) Show a simple protocol with an attack that is based on a collision. 2. Even though the birthday paradox can still be used for constructing collisions, why is it in a practical setting much harder to construct them for MACs than for hash functions? Since this is the case: what security is provided by a MAC with 80-bit output compared to a hash function with 80-bit output

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