From: J. Michael Diehl <mdiehl@triton.unm.edu>
Date: Sat, 5 Jun 93 15:06:37 PDT
To: smb@research.att.com
Subject: Re: Dig. Cash Question.
In-Reply-To: <9306052136.AA04744@triton.unm.edu>
Message-ID: <9306052206.AA05155@triton.unm.edu>
MIME-Version: 1.0
Content-Type: text/plain


According to smb@research.att.com:
> 
> 	I'm reading the paper that was announced on this list about
> 	Digital Cash last week.  It was writen by Stefan Brands.  I
> 	think I have a strong Math background, but I don't know what is
> 	meant by a "descrete log" in a group G.  I understand what a
> 	group is.  I just don't know what properties an element, a,
> 	would have if it were the log sub p of e.  Can someone help
> 	me.  Otherwise, this is a very interesting article.  Thanx in
> 	advance.
> 
> You might want to fix your mailer; according to the strict letter of
> RFC822, human-readable names shouldn't contain periods unless quoted....

I sent word to those "in charge." ;^)
Maybe after I graduate, they will fix it....

> Anyway -- suppose that in some group, you know that a^n=b, where a
> and b are members of the group, and n is an integer.  a^n indicates
> the group operation iterated n times.  The discrete log problem is
> recovering n, given ``a'' and a^n=b.
> 
> In some groups, this is a very hard problem.  The group most commonly
> used in cryptography is the field GF(p), i.e., the field of integers
> modulo p, where p is some large number, preferably a prime, and ``a''

If I understand this correctly, if p is not a prime, then n may not be unique.

> is a ``primitive root'' of the field.  The problem is thus to find
> n, given ``a'' and a^n modulo p.  Other instances of discrete log
> are useful as well; NeXT, for example, uses the same basic equation
> in a field over some family of elliptic curves.  Their much-ballyhooed
> invention was to find a set of such curves for which the exponentiation
> operation can be performed very efficiently.
> 
Thanx for the (very!) clear explaination.

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