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One can be fascinated by the simplicity of the schemes created by Ralf Merkle; like the Merkle tree or his key negociation protocol over an insecure channel.

Wikipedia has some material on "Merkle puzzles" (wikipedia_page) and his seminal paper can be found online (article_pdf).

But, could this venerable construction be put to use in order to reach nowadays security strength requirements (i.e. a key of at least 128 bits strength, or even 256 bits for the real paranoids out there).

Thanks!

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The complexity required for the attacker to break the scheme is at maximum quadratic in the security parameter $n$. It is not enough for a secure cryptographic protocol where you want exponential complexity to break the scheme.

Say $n$ is the difficulty of solving the puzzles and $m$ is the number of puzzles. Alice needs to solve one puzzle in time $O(n)$ but Bob will need to look in his puzzles to find the correct key. He needs roughly $O(m)$ time. The scheme has then $O(n+m)$ time complexity.

For breaking the scheme, Eve can brute force all the puzzles, she then needs $O(nm)$ time complexity. If you want to have this complexity be around $2^{128}$ you need to send an incredible amount of puzzles and/or puzzles too hard.

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