MathCryptography

The discrete logarithm problem

Logarithm of product

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Select the correct formula for $\log_{g}(h_{1}h_{2})$ in $\mathbb{Z}^{*}_{p}$ .

Tip: How many elements are there in $\mathbb{Z}^{*}_{p}$ ? What can we say about $g^{x}$ and $g^{y}$ if $x - y$ is a multiple of this number?

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\log_{g}(h_{1}h_{2}) = \log_{g}h_{1} + \log_{g}h_{2}

\log_{g}(h_{1}h_{2}) = \log_{g}h_{1} \cdot \log_{g}h_{2} \bmod (p - 1)

\log_{g}(h_{1}h_{2}) = \log_{g}h_{1} \cdot \log_{g}h_{2}

\log_{g}(h_{1}h_{2}) = (\log_{g}h_{1} + \log_{g}h_{2}) \bmod (p - 1)

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