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Checking if a function is collision-resistant

dk flag

Consider a prime order cyclic group $\Bbb G$ of order $q$ with generator $g$. Then consider the function$$f:\Bbb Z^n_q\to\Bbb G\\(\alpha_1,\alpha_2,...,\alpha_n)\mapsto g^{\alpha_1\cdot\alpha_2...\cdot\alpha_n}$$

Is this function collision resistant with any of CDH/DDH/DLog assumptions in $\Bbb G$?

I think $f$ is not collision-resistant as it is easy to find two inputs that map to the same output. Namely $f(\alpha_1,\alpha_2,...,\alpha_n)=f(\alpha_n,\alpha_{n-1},...,\alpha_1)$. Is this the correct logic?

poncho avatar
my flag
Why would you expect that not to be correct? Does it meet the criteria of a collision (that is, two different valid messages that 'hash' to the same value)?
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