Cryptology: consider Diffie-Hellman key exchange scheme with

G

Ghostgirl

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Hey folks, not sure where to post this so I'll try it here... sorry in advance if its the wrong area. I am trying to get a better understanding of the math theory behind some of the technologies I configure at my part time job, so I have been working on some examples I found in an old textbook and this one I do not understand.

My problem is as follows:

Consider a Diffie-Hellman key exchange scheme with a common prime q = 11 and a primitive root a = 7. That is, we calculate values to send across the insecure channel by using 7[sup:2441xkzt]x[/sup:2441xkzt] (mod 11). Assume that User A uses the Diffie-Hellman scheme to establish a secure channel with User B.

(a) If user A has public key Y[sub:2441xkzt]A[/sub:2441xkzt] = 9, what is A’s private key X[sub:2441xkzt]A[/sub:2441xkzt]?

(b) If user B has public key Y[sub:2441xkzt]B[/sub:2441xkzt] = 3, what is the shared secret key SK?

I am not really sure how to to start part a) or b) yet, I know the Diffie-Hellman algorithm is based on the complexity of the reverse process of computing a power modulo a large prime number, and that it is used to set up a shared key between 2 entities on an insecure line which is in turn used to encrypt following messages, but I am not up much on the math theory behind it (I just have experience with the practical implementations in networks). Any help is appreciated :D

Thanks,
GG
 
Re: Cryptology-Related Math Problem

Yes I have read a lot of the theory online about Diffie-Hellman already, I just need an example solved step by step so I can work on the other 30 or so problems using this one as leverage, I have little background in the math theory so details would be helpful.

Thanks,
GG
 
Re: Cryptology-Related Math Problem

That would be semester worth of course in Advanced Discrete Mtahematics - not relly feasible inn this format.
 
Re: Cryptology-Related Math Problem

Okay, well I understand the mod function and the terms common prime and primitive root. All I really need is the method of solving this example question to go about doing the other ones I decided to try, I should be able to teach myself after I get the basic structure of how to get User A's private key and the shared secret key if given the information stated in the problem.

Thanks,
GG
 
Ghostgirl said:
I have little background in the math theory so details would be helpful.
Click to expand...
Subhotosh Khan said:
That would be semester worth of course in Advanced Discrete Mtahematics....
Click to expand...
Ghostgirl said:
I should be able to teach myself after I get the basic structure....
Click to expand...
Teaching yourself is generally even harder than having somebody knowledgeable explain the material to you. :shock:

Since you haven't been able to make any headway, you say, in understanding how the relevant material applies to this exercise, the tutor's recommendation may be the best option: Enroll in a course, or sequence of courses, which covers the necessary foundational concepts and then teaches the specific terms and techniques necessary to this area of study. :idea:

Either way, please accept our well-wishes on your studies! :D

Eliz.
 
Re: Cryptology-Related Math Problem

Okay I have been working on part a), here's what I have so far

- where X[sub:2qc9u13v]A[/sub:2qc9u13v] is User A's private key, q is the common prime, Y[sub:2qc9u13v]A[/sub:2qc9u13v] is the public key and a is the primitive root :
X[sub:2qc9u13v]A[/sub:2qc9u13v] = q[sup:2qc9u13v]Y[sub:2qc9u13v]A[/sub:2qc9u13v][/sup:2qc9u13v] (mod a)
= 1[sup:2qc9u13v]9[/sup:2qc9u13v] (mod 7)
= 1 X (mod 7)
= 1
- are there any glaring errors so far? I don't understand how I'm supposed to use the 7[sup:2qc9u13v]x[/sup:2qc9u13v](mod 11) part in this answer
 
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