Score:1

How to calculate a common encryption key between sender and receiver

pt flag

In the picture below, for the text underlined in red color: 7X(MOD 11) = 72(MOD 11) =49(MOD 11)

My questions are:

(1) obviously there is no equal relationship between 72(MOD 11) and 49 (MOD 11), and where does 49 come from?

(2) X and Y are picked up randomly, are 7 and 7 in 7X and 11 in MOD 11 also picked up randomly, or is it some algorithm? there is no any explanation in the textbook I have

(3) in the text marked in blue color, where does 2401 come from?

enter image description here

Score:2
in flag

(1) obviously there is no equal relationship between 72(MOD 11) and 49 (MOD 11), and where does 49 come from?

It's not $72$, it's $7^2 = 7 \cdot 7 = 49$.

(2) X and Y are picked up randomly, are 7 and 7 in 7X and 11 in MOD 11 also picked up randomly, or is it some algorithm? there is no any explanation in the textbook I have.

No, they are not random. This is simply the Diffie-Hellman algorithm. 7 is the base (or generator) and 11 is the modulus. These are pre-established configuration parameters.

Of course, to be secure, they need to be a whole lot larger - about 2048 bits or higher for the modulus.

(3) in the text marked in blue color, where does 2401 come from?

Similar, this is bad printing, it's just $7^4$.

Maarten Bodewes avatar
in flag
Sorry, I'm in answering mode - should have left this for a newcomer.
common2k avatar
pt flag
it is very clear and thanks
Maarten Bodewes avatar
in flag
You're welcome. By the way, if you use WolframAlpha and enter 2401 you get [this page](https://www.wolframalpha.com/input/?i=2401) with the nice remark: "$2401 = 7^4$ is a perfect $4^{th}$ power."
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