🚀 go-pugleaf

In article <1992Aug27.111639.16325@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
> :Why are you trying to discourage people from
> :entering the RSA-129 contest, Bob?
> Now this last accusation really is obnoxious, because it puts words
> in my mouth that I have never said.

Bob, you stated that a 6-7 digit improvement in GNFS polynomials in this
range would result in only a 2x speedup. If this were true, it would put
a rather small cap on the possible benefits of the RSA-129 contest.

It is not, in fact, true. It is wildly inaccurate: as I pointed out
before, such an improvement could easily gain an order of magnitude in
speed. (For instance, p(9) is more than ten times p(10), p being the rho
function; here N(a,b) is compared to (max AFB)^9.) You had your chance
to retract the statement, Bob, and you failed.

Someone who believed your misstatement about speedups would obviously be
discouraged from entering the RSA-129 contest. Bob, what's your
motivation? Why are you trying to squash interest in GNFS? You're
achieving the effect of lying to the public, even if you don't mean to
do so. I don't care whether it's obnoxious of me to point this out---I
can't sit by and watch you corrupt the views of people who haven't
learned about GNFS and can only go by what they hear from others.

> All you are doing is gainsaying my data without posting data of your own.

That's right. The bulk of data which I have is part of an article I'm
writing with Arjen Lenstra on our GNFS implementation. That data, like
your data, is not sufficient to conclude that GNFS will probably be
slower than MPQS at 129 digits. Yet you keep stating this conclusion.

> you are confusing the two functions.

My apologies. I mistakenly thought that you were talking about Dickman's
rho function, which (I can say with some assurance now that I've checked
my references) a few people attribute to Knuth and Trabb Pardo (because
Knuth and Trabb Pardo did publish some things about it).

I guess you are referring to the logarithmic sum that Schroeppel
originally suggested for choosing multiples for the continued fraction
method. If so, I am astounded at your statement that it would be nice to
have such a function for the algebraic side of GNFS---everyone knows
what it is, namely the sum of log p times the (easily computable)
probability that a coprime pair a,b has N(a,b) divisible by p^d, over
all p and d.

---Dan