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This sounds like "fair exchange," the subject of many good research papers. In general you need a third party to give any security guarantees, but "optimistic fair exchange" involves the third party only when one of the parties tries to cheat (i.e., when both play honestly there is no involvement from the third party). Incidentally, Diffie-Hellman is most ...


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In general, no. There are: $$ {2^{64} \choose 2^n} = \frac{2^{64}!}{2^{n}!(2^{64}-2^n)!} $$ possible ways of selecting $2^n$ distinct 64-bit vectors. This is a huge number; using Stirling's approximation of factorials, when $2^{n}$ is substantially smaller than $2^{64}$ (i.e. when $n$ is smaller than $55$ or so), this number of combinations is approximately ...


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Sketch. Suppose you have an adversary against the composed scheme with advantage $\epsilon_3$. Observe that whenever you have a signature for the composed system, you have a signature for each of the three component signature schemes. It should then follow that a forger for the composed signature scheme can be turned into a forger for each of the three ...


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I believe this can be reduced to a case of format-preserving encryption. http://en.m.wikipedia.org/wiki/Format-preserving_encryption Using one of the many algorithms for FPE, you should be able to do such a mapping. EDIT: As Seth points out in the comments to my original answer, the "cycling" method of FPE doesn't work here, but the first method described ...



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