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The following archive was created by hippie-mail 7.98617-22 on Thu May 27 1999 - 23:44:21
Paulo Barreto (pbarreto@nw.com.br)
Tue, 06 Apr 1999 22:26:12 -0300
At 09:17 1999.04.06 -0400, Ge' Weijers wrote:
>So the question is: what is 'the keylength' when you use a generator g
>of order q, such that (e.g.) |q| = 160 bits, and a modulus |p| =
>1024. The private key x has a length of 160 bits, but the public key
>g^x has a length of 1024 bits. My vote goes to the length of g^x, as
>that seems to determine the work factor for an attacker as long as q
>is in a suitable range.
Aha! But you could equally vote for the length of x, as that seems to
determine the work factor for an attacker as long as p is in a suitable
range (for instance, it's futile to choose |p| = 2048 while keeping |q| =
160).
The fact is that both q = 160 and p = 1024 determine the work factor for an
attacker, namely O(2^80).
When working with elliptic curves the answer seems to be easier, as the
order of the cyclic group generator, the curve order, and the underlying
finite field dimension are nearly the same size in practice.
Paulo.
The following archive was created by hippie-mail 7.98617-22 on Thu May 27 1999 - 23:44:21