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The screenshot from a book with Chaum–Pedersen Protocol description is below.

Chaum–Pedersen Protocol description

I'm trying to implement it for my own. And I don't get math here.

My assumptions:

  1. Discrete Logarythm functions:

Discrete Logarythm

  1. The dot in the formula below is a usual multiplication: 2 • 2 = 4

Examples:

Example 1

Example 2

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Your parameters do not satisfy the assumptions for the protocol.

To have $g$ and $h$ generate groups of prime order $q$ they must belong to such a group.

So $q$ (which in reality must be picked large enough for DL to be hard) must be a prime larger than both $g$ and $h$. So $q$ must be larger than 7919.

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  • $\begingroup$ Thanks! You're definitely right. Also, I found the same question with great explanation. $\endgroup$ Commented Mar 28, 2022 at 10:16

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