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pair wise independent hash function

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Let H be a pairwise independent hash function family with key space K, input space {0, 1}ℓ and output space {0, 1}ℓ. Use H to construct an encryption scheme with message space {0, 1}ℓ such that the scheme satisfies O(2−ℓ)-perfect two-time security. (Note: your encryption scheme must be stateless.) You must provide a detailed proof of security, including appropriate hybrid experiments. 1-3

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ng flag
Sounds like coursework. Show us what you have tried and what your thoughts are, then we might be able to provide you with hints.
fgrieu avatar
ng flag
If you want help on this cut&paste of homework/exercise, first [edit](https://crypto.stackexchange.com/posts/107792/edit) it to bring it to a readable form, preferably [using LaTeX](https://crypto.meta.stackexchange.com/a/1070/555). Reword it so that's it's no longer a verbatim (thus a possible copyright violation) and in the style of direct instructions to a student. State what you have tried or/and where you are stuck. If that's at start, state/summarize the definitions of the notions (pairwise independent hash function family, two-time security of a stateless encryption scheme).
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