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However, in some protocols descriptions, like TLS 1.3, I find them say the client sends "hello message includes Diffie-Hellman public values for the client's preferred groups". What is "group" refers to?? The term group is a mathematical concept that guarantees that a specific operation doesn't leave a set, that it is associative, that there is a ...


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No, it's no easier than the standard DBDH problem. Here's the reduction that shows that: suppose that we have an Oracle that solves your problem (given $g^s, g^y, g^r, g^t, g^{st-rs}, g^{(yr+d)/t}, e(g,g)^x$ is $e(g,g)^x = e(g,g)^{syr}$?) Now, suppose we're given $g^s, g^y, g^r, e(g,g)^x$, and are asked whether $e(g,g)^x = e(g,g)^{syr}$. What we do is ...



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