Remainder class group is a type of grouping that is used in mathematics to identify the numbers that are left over after a division problem.

Exponential Map

$g^{(*)}: Z_n \rarr Gx \rarr g^x$

g is generator.

We use the remainder class group to map to a group law G. In the group law of G, we do exponential

This works because

Def1: e → e

Def2: $g^{x+y} = g^x * g^y$

Two ways to map:

1. first compute in $Z_n$ then apply exponential map to result
2. apply exponential map first, being in G, then you can apply group law in G
   1. Why it works? Because of Def1 and Def2

Log Map

$\log_g(*) = G \rarr Z_nx \rarr \log_g(x)$

We are doing opposite, going from group G to some remainder class group.

base g is the generator??

We have no way to comppute this map, only can try all elements in group G until we find correct value $\log_g(x)$

<aside> 💡 Why is it harder to do log? Because exponential operations such as add, mult, then MODDING is super easy. modding is what obfuscates the computation trace so that its hard to trace back to beginning, which is what log map is doing.

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