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. +-----------------------+-----------------------------+---------+ | J. Michael Diehl ;-) | I thought I was wrong once. | PGP KEY | | mdiehl@triton.unm.edu | But, I was mistaken. |available| | mike.diehl@fido.org | | Ask Me! | | (505) 299-2282 +-----------------------------+---------+ | | +------"I'm just looking for the opportunity to be -------------+ | Politically Incorrect!" <Me> | +-----If codes are outlawed, only criminals wil have codes.-----+ +----Is Big Brother in your phone? If you don't know, ask me---+