line sieving references

[Raman]

Lattice sieving has been explained within "Development of Number Field Sieve"
Question → Is the sieving method as explained as within "Prime Numbers - A computational perspective" line sieving?
If not, where could I find out furthermore about line sieving?

Thanks to you
Merci (within French language) :smile:

[jasonp]

Yes, Crandall and Pomerance describe line sieving.

The thesis here has a good description of line sieving, along with a complete small example.

[LaurV]

Originally Posted by jasonp

Yes, Crandall and Pomerance describe line sieving.

The thesis here has a good description of line sieving, along with a complete small example.

The thesis is very good (especially chapter 6!), it is taking you through all the steps of "factorization", from its basic to the most complex, so it is a must to read, but read it with caution, it has few "small omissions" an lost ends. For example, right in the beginning, according to the definition 2.2 on page 6, there are no prime numbers. I can prove all numbers are not prime. (I did not say "composite"). (for a proof just take b=-ka for any integer k>0)

[henryzz]

Originally Posted by LaurV

The thesis is very good (especially chapter 6!), it is taking you through all the steps of "factorization", from its basic to the most complex, so it is a must to read, but read it with caution, it has few "small omissions" an lost ends. For example, right in the beginning, according to the definition 2.2 on page 6, there are no prime numbers. I can prove all numbers are not prime. (I did not say "composite"). (for a proof just take b=-ka for any integer k>0)

That is picking holes too much. It is a minor mistake though. It should limit b to the positive integers rather than the integers.

[R.D. Silverman]

Originally Posted by LaurV

The thesis is very good

As a superficial survey paper, I agree with the above statement.

However, it is nothing more than that. It appears to have been done
as a Master's thesis. But it contains no original work and the presentations
omit many (important!) details.

All of Chapter 2 should be omitted. It contains material that should be
assumed for a graduate level thesis. Any potential reader would know
the material.

I would not accept it as a Master's Thesis if I were asked to review it.
It is too superficial and elementary.

[jasonp]

PGNFS was the only place I could find that went through all the steps for computing the NFS algebraic square root using the brute force method. There are optimizations that it doesn't mention, but those optimizations appear in 'The Development of the Number Field Sieve'

[LaurV]

Originally Posted by R.D. Silverman

As a superficial survey paper, I agree with the above statement.

Well, correction to what I said: the thesis is very good for my level of knowledge. You won't expect all of us to know the things you know, in that case we won't need any thesis to read..

[Raman]

Originally Posted by R.D. Silverman

I would not accept it as a Master's Thesis if I were asked to review it.
It is too superficial and elementary.

I think the student would have discussed with the mentor about structure of his master's thesis before writing it. If it was not worthy as a master's thesis, the mentor would have stopped him before itself. Perhaps this was assigned by his mentor to be written as a master's thesis.

Originally Posted by R.D. Silverman

It appears to have been done
as a Master's thesis. But it contains no original work and the presentations
omit many (important!) details.

Suppose you are a Master's student, and you have some interesting problem in your mind which you want to explore on your own , and feel confident that you can come up with new, interesting, creative ideas, not sure if important.

And then would you go with that for your Master's thesis, or will you go for your mentor's input? He gives you a problem he has in his mind that you find it difficult to come up with new innovative ideas, or is based on writing a report, a summary of what is already known. I think that you will respect your mentor's ideas, as he has experience with importance of problems chosen for master's thesis. As a student, you will have no idea as how far your ideas are worthwhile.



I have decided to put Ph.D on hold, I am doing M.Phil right now. After to my M.Tech degree. Afterwards to after towards switching disciplines. I think it is not a good idea to rush to a Ph.D thesis which will turn out into low quality if I work towards commitment for some monthly stipend, compulsory submission after provided deadline.

Good idea is to read targetted books, attend targetted course work, first submit small papers into some technical journal, conference first, gain some experience, afterwards go towards Ph.D thesis, which will be merger of all work. I think it is not a good idea to rush to a Ph.D thesis. I aim submitting some paper with my mentor towards some technical journal. This is integer factorization, as I have topic of quadratic forms representation - uses some of ideas from integer factorization as topic

[chris2be8]

I think this thread should be in the Factoring forum, not the NFSNET Discussion forum since it has nothing to do with NFSNET. Could some moderator please oblige?

Chris

[jasonp]

ok.

The novelty required in a Master's thesis varies widely, and by field. My own involved a lot of original code but was just a performance comparison of various new cryptographic schemes.

[R.D. Silverman]

Originally Posted by jasonp

ok.

The novelty required in a Master's thesis varies widely, and by field. My own involved a lot of original code but was just a performance comparison of various new cryptographic schemes.

Perhaps. But I will assume that you did your own analysis, rather than
just quoting work done by others. And you wrote your own code.

The thesis under discussion was nothing more than a compilation of
information from other sources. While academic standards vary,
a simple transcription of information available from other sources
does not meet what I consider to be a reasonable standard for a
graduate level thesis.