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Re: Dig. Cash Question.
According to [email protected]:
>
> 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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