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I cannot understand how this works.

$\text{A}_\text{public} = g^a \bmod p$

$\text{B}_\text{private} = \text{B}$

$\text{g} = p$

I also have $p$, I need to get the shared key, that I know both $\text{A}$ and $\text{B}$ get exactly the same value. Im not understanding how can I get the shared key that $\text{B}$ generated only having those variables I wrote above.

Also I know that the shared key is $\text{g}^\text{ab} \bmod p$, how can I get that $\text{b}$ value?

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1 Answer 1

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$\text{B}_\text{private}$ is $\text{b}$ and $\text{B}_\text{public}$ is $\text{g}^\text{b} \bmod p$.

So $\text{B}$ can compute $(\text{A}_\text{public})^b \bmod p = \text{g}^{\text{ab}} \bmod p$

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  • $\begingroup$ thanks, how am I supposed to calculate that with a 617 digit p? its very large and this is not working $\endgroup$ Aug 27, 2019 at 13:16
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    $\begingroup$ In Python you can use $\mathrm{pow}(\mathrm{publicA}, b, p)$. For others, you can use big numbers library like GMP. $\endgroup$
    – user69015
    Aug 27, 2019 at 13:19
  • $\begingroup$ I feel like a complete stupid, I love you guys! Thanks for the help, for real. $\endgroup$ Aug 27, 2019 at 13:27
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    $\begingroup$ The library has vulnerable to timing/power attacks. It is not designed against. $\endgroup$
    – kelalaka
    Aug 27, 2019 at 16:26
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    $\begingroup$ @Conrado For cryptographic purpose, it is better that computations (multiplication, squaring, inversion) are done in constant-time to avoid leaking information. Thanks kelalaka for pointing that. $\endgroup$
    – user69015
    Aug 27, 2019 at 17:05

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