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As I look upon Burmester Desmedt algorithm:

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I notice that the intermediate key $K_i$ is getting calculated as:

$K_i=(k_{i+1}/k_{i-1})^{x_i} \mod p$

Thus I wonder wheher the division $k_{i+1}/k_{i-1}$ should result an integer of a floating point number.

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Thus I wonder whether the division $k_{i+1}/k_{i-1}$ should result an integer of a floating point number.

An integer.

Specifically, this computation is done modulo $p$; that is, the result of this division is the value $d$ such that $d \cdot k_{i-1} \equiv k_{i+1} \pmod p$.

One way to find this $d$ is to compute the multiplicative inverse of $k_{i-1}$ modulo $p$ (for example, using the Extended Euclidean algorithm, and then multiply that inverse with $k_{i+1}$ (again, modulo $p$)

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  • $\begingroup$ What I actually do is I permform the division with OpenSSL's BigInt so I wanted to clarify wheher is this way to go. $\endgroup$
    – Dimitrios Desyllas
    Commented Feb 13, 2019 at 19:01
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    $\begingroup$ @DimitriosDesyllas: you mean BN_div? No, that's wrong; you need to do division in the field $\mathbb{Z}_p$, not in the ring $\mathbb{Z}$ (rounded down). Instead, see BN_mod_inverse and BN_mod_mul $\endgroup$
    – poncho
    Commented Feb 13, 2019 at 19:32
  • $\begingroup$ So I calculate inverse of the $k_{i-1}$ with BN_mod_inverse And then I multiply it with BN_mod_mul? $\endgroup$
    – Dimitrios Desyllas
    Commented Feb 13, 2019 at 20:58
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    $\begingroup$ @DimitriosDesyllas: by George, I think you've got it... $\endgroup$
    – poncho
    Commented Feb 13, 2019 at 21:01

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