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2

Because groups used for Diffie-Hellman cannot be given a non-trivial, efficiently calculable metric, you cannot define such things like a "local maximum" or "local minimum". You also cannot say if you are climbing or diving.

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NO, we can't apply an hill-climbing algorithm to Diffie–Hellman. In order to break Diffie-Hellman key exchange, it is enough for Eve to reverse exponentiation modulo the public prime $p$; that is, given $g^x\bmod p$, find $x$. That's the Discrete Logarithm Problem. We do not know that hill-climbing can help for that (or the slightly less general DH ...

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Depends on how you define the function. A perfect hash function is a bijection from an input set onto a set of integers. However, that set of integers is not necessarily a continuous range, unless you have a minimal perfect hash function. So if you define the function as mapping a particular set to e.g. $\mathbb{N}$ or $[1, n]$ where $n$ is larger than the ...

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The injective hash function wikipedia referes to is not a secure hash function for cryptographic purposes. It is a hash function used for fast database access. An ideal secure hash function is a random oracle and a random oracle is not injective with very high probability.

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No, it is not always bijective. A perfect hash guarantees that no two inputs (from the set of valid inputs) collides, so it is clearly a 1 to 1 mapping. However, in the case where the output range contains more possible values than there were valid inputs, there will be outputs which do not map back to inputs. hence it is not bijective. If you restrain ...

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Grover's algorithm treats the function it is evaluating as a black box and finds, with high probability, an input to the black box such that it outputs a specified value in $O(N^{1/2})$ evaluations of the function. Since Grover's algorithm works on the function as a black box, your modification does not hinder Grover's algorithm at all in finding the ...

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As I noted in another answer, Auguste Kerckhoffs published his principles in the scientific/academic journal “Journal des sciences militaires, vol. IX, pp. 5–38 in his article "II. DESIDERATA DE LA CRYPTOGRAPHIE MILITAIRE.", Jan. 1883. So, when you ask since when academics and cryptographers “might” have been accepting (and even applying) those rules, the ...

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There is a simpler way: implement a stream cipher using the hash function, and use that to encrypt the plaintext. Probably the most used stream mode is counter (CTR) mode, which is normally defined for block ciphers. CTR mode works equally well with a PRF (MAC) as with a PRP (block cipher). It only uses the function as a one-way function; with a block ...

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The numbers $n$ (coding source) and $m$ (coding index for a given source) can be combined into a single bitstring; e.g. with $0\le m<2^u$ and $0\le n<2^v$, as a bitstring of $\lceil u+v\rceil$ bits. Then, converting that single bitstring into a unique random-like number can be done by encryption with a secure block cipher with block width $w\ge u+v$ ...

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