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A one-way permutation is just a one-way function in which the function is a permutation (id est, a bijective function). Every OWP is a OWF, the converse is not true. IND-CPA security is a security notion specifically related to encryption schemes. OWF and OWP are not encryption schemes, hence they cannot be said "IND-CPA secure"; however, one can construct ...

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Sure. one-way permutation ​ + ​ strong hard-core functions $\to$ pseudorandom generator $\to$ stream cipher The keystream is concatenation of the strong hard-core function's values at the iterates of the one-way permutation on the key. ​ ( k,f(k),f(f(k)),f(f(f(k))),... )

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Assuming that there are no collisions and there exists a 1 to 1 bijection between input and output, you could construct and store a table of assignments on a single round of encryption for all 256 possible bytes regardless of the key size. From there you can extend this to subsequent rounds by simply XORing the result of the previous round to the next 8 bit ...

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