# Tag Info

3

You'd need to compute $K^{(a^{-1})}$. Only those who hold the private key $a$ can do this. Multiplying with $(g^a)^{-1} = g^{-a}$ would subtract $a$ from the exponent, not divide the exponent by $a$. So your optimization isn't possible in practice. Take a look at the alternatives at Can one generalize the Diffie-Hellman key exchange to three or more ...

3

Even if you were doing that you would only ensure that the communication between you and "some" router is secure. It's still possible to MITM using arpspoof for instance such that in: [you] <--- A ---> [hacker] <--- B ---> [router] Communications A & B are encrypted, yet you're not talking to the real router.

2

Why are there exactly $m$ values for $k$? Well, assuming $k$ is the value of the shared secret that either Alice and Bob derive, well, that's not true; there are at most $m$ possible values, however it may be fewer. There will be exactly $m$ values if $g$ is a primitive root modulo $p$; however when we use Diffie-Hellman in practice, we generally avoid ...

2

PKCS#3 is an older standard which only defines the DH primitive itself. It contains the following information: parameter generation, the Diffie Hellman key agreement algorithm, integer/octet string conversions (as in PKCS#1, RSA) and the specification of an ASN.1 structure for the parameters. The ASN.1 structure is very limited, containing only the necessary ...

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