a question about Diffie-Hellman key exchange mode

[William Cai-6]

Hi list,

I get a question regarding Diffie-Hellman key exchange of SSL. Not sure
if this is the right place for such question. But this could be an easy
one for those who are familiar with SSL protocol. :-) Below is cited
from William Stallings' paper.

------------------------- cited from Internet
-------------------------------
Fixed Diffie-Hellman: This a Diffie-Hellman key exchange in which the
server's certificate contains the Diffie-Hellman public parameters
signed by the certificate authority (CA). That is, the public-key
certificate contains the Diffie-Hellman public-key parameters. The
client provides its Diffie-Hellman public key parameters either in a
certificate, if client authentication is required, or in a key exchange
message. This method results in a fixed secret key between two peers,
based on the Diffie-Hellman calculation using the fixed public keys.
----------------------- end of the citation -------------------------

According to my understanding, Diffie-Hellman algorithm is based on
something like this,
1. public prime number, p
2. public base, g
3. Side A's private key, a
4. Side A's public key, A = g ^ a mod p
5. Side B's private key, b
6. Side B's public key, B = g ^ b mod p

The question is that which items above the Diffie-Hellman public
parameters consist of? If they are 1, 2 and 4, then we need at least an
additional step pass the public prime number and public base to the
other side, otherwise, the other side cannot calculate its public key.
right? But I don't see such description in the paper. Are public prime
number and public base presetted?

Any response is appreciated!

Thanks,
William
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[Michael Sierchio]

William Cai wrote:

> According to my understanding, Diffie-Hellman algorithm is based on
> something like this,
> 1. public prime number, p
> 2. public base, g
> 3. Side A's private key, a
> 4. Side A's public key, A = g ^ a mod p
> 5. Side B's private key, b
> 6. Side B's public key, B = g ^ b mod p
>
> The question is that which items above the Diffie-Hellman public
> parameters consist of? If they are 1, 2 and 4, then we need at least an
> additional step pass the public prime number and public base to the
> other side, otherwise, the other side cannot calculate its public key.
> right? But I don't see such description in the paper. Are public prime
> number and public base presetted?

Yes, the p and g are well known and agreed upon in advance.


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[William Cai-6]

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Thanks Michael! Could you please share me some information about when/how to agree upon p & g?

Thanks,
William

---

From: Michael Sierchio <kudzu@...>
To: openssl-users@...
Sent: Sunday, July 5, 2009 11:58:42 PM
Subject: Re: a question about Diffie-Hellman key exchange mode

William Cai wrote:

> According to my understanding, Diffie-Hellman algorithm is based on
> something like this,
> 1. public prime number, p
> 2. public base, g
> 3. Side A's private key, a
> 4. Side A's public key, A = g ^ a mod p
> 5. Side B's private key, b
> 6. Side B's public key, B = g ^ b mod p
>
> The question is that which items above the Diffie-Hellman public
> parameters consist of? If they are 1, 2 and 4, then we need at least an
> additional step pass the public prime number and public base to the
> other side, otherwise, the other side cannot calculate its public key.
> right? But I don't see such description in the paper. Are public prime
> number and public base presetted?

Yes, the p and g are well known and agreed upon in advance.


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[PMHager]

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William,

 

have a look at MODP (Modular Exponential DH Groups) referenced in RFC5246:

 

RFC2409 defines primes for 768 and 1024 bit, and

RFC3526 defines primes for 1536, 2048, and 3072 bit.

(The generator is always 2.)

 

Peter-Michael

---

From: owner-openssl-users@... [mailto:owner-openssl-users@...]   On Behalf Of William Cai
Sent: Monday, July 06, 2009 3:25 AM
To: openssl-users@...
Subject: Re: a question about Diffie-Hellman key exchange mode

Thanks Michael! Could you please share me some information about when/how to agree upon p & g?

Thanks,
William

---

From: Michael Sierchio <kudzu@...>
To: openssl-users@...
Sent: Sunday, July 5, 2009 11:58:42 PM
Subject: Re: a question about Diffie-Hellman key exchange mode

William Cai wrote:

> According to my understanding, Diffie-Hellman algorithm is based on
> something like this,
> 1. public prime number, p
> 2. public base, g
> 3. Side A's private key, a
> 4. Side A's public key, A = g ^ a mod p
> 5. Side B's private key, b
> 6. Side B's public key, B = g ^ b mod p
>
> The question is that which items above the Diffie-Hellman public
> parameters consist of? If they are 1, 2 and 4, then we need at least an
> additional step pass the public prime number and public base to the
> other side, otherwise, the other side cannot calculate its public key.
> right? But I don't see such description in the paper. Are public prime
> number and public base presetted?

Yes, the p and g are well known and agreed upon in advance.


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[William Cai-6]

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1


Got it. Thanks for answering such a naive question to a newbie. :-)
Really appreciate your help.

PMHager wrote:

> William,
>  
> have a look at MODP (Modular Exponential DH Groups) referenced in RFC5246:
>  
> RFC2409 defines primes for 768 and 1024 bit, and
> RFC3526 defines primes for 1536, 2048, and 3072 bit.
> (The generator is always 2.)
>  
> Peter-Michael
>
> ------------------------------------------------------------------------
> *From:* owner-openssl-users@...
> [mailto:owner-openssl-users@...]   *On Behalf Of *William Cai
> *Sent:* Monday, July 06, 2009 3:25 AM
> *To:* openssl-users@...
> *Subject:* Re: a question about Diffie-Hellman key exchange mode
>
> Thanks Michael! Could you please share me some information about
> when/how to agree upon p & g?
>
> Thanks,
> William
>
> ------------------------------------------------------------------------
> *From:* Michael Sierchio <kudzu@...>
> *To:* openssl-users@...
> *Sent:* Sunday, July 5, 2009 11:58:42 PM
> *Subject:* Re: a question about Diffie-Hellman key exchange mode
>
> William Cai wrote:
>
>> According to my understanding, Diffie-Hellman algorithm is based on
>> something like this,
>> 1. public prime number, p
>> 2. public base, g
>> 3. Side A's private key, a
>> 4. Side A's public key, A = g ^ a mod p
>> 5. Side B's private key, b
>> 6. Side B's public key, B = g ^ b mod p
>>
>> The question is that which items above the Diffie-Hellman public
>> parameters consist of? If they are 1, 2 and 4, then we need at least an
>> additional step pass the public prime number and public base to the
>> other side, otherwise, the other side cannot calculate its public key.
>> right? But I don't see such description in the paper. Are public prime
>> number and public base presetted?
>
> Yes, the p and g are well known and agreed upon in advance.
>
>
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> <mailto:openssl-users@...>
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- --
PGP Key: http://pgp.mit.edu:11371/pks/lookup?op=vindex&search=0x76E957AF
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