Question

Am I setting this up correctly?

A/B are using the Diffie-Hellman Key Exchange Protocol with public modulus N = 1601 and public base e = 23. A sends B 1596 and B sends A 403.

Answer 1

\(23^x \mod 1601 \equiv 1596\\23^x \mod1501 \equiv 403\)

Answer 2

you want to figure out the secret key ?

Answer 3

yeah, I'm getting different numbers when I try setting it up this way

Answer 4

using this as a reference

Answer 5

oh nevermind, I got it. 1028

Answer 6

how ?

Answer 7

I kinda cheated using wolfram. \(23^x \mod 1601 \equiv 403 \implies x=1600n+191\)

1596^191 mod 1601 = 1028

if you want an algorithmic approach, we're meant to be using pohlig-hellman or baby sttep giant step

Answer 8

it goes the same way in reverse. \(23^x \mod 1601 \equiv 1596 \longrightarrow x=1600n+76\)

403^76 mod 1601 = 1028

Answer 9

1596^x = 403^y mod 1601

right ?

Answer 10

correct

Answer 11

yes so the secret key is 1028

Answer 12

Thanks rational :D