I'm new to Function Field Sieve(FFS) (Number Field Sieve(NFS) as well) method and I'm finding it is quite difficult to understand it (especially concepts of valuation at infinity, Ca,b curves etc.)

I have read these papers:

(Leonard Adleman 1994: The function field sieve), Razavan: 2^809 using Function Field Sieve , Joux: Function Field is quite special.

For NFS luckily i got this book : Chapter 11 NFS (Algebraic Number Theory : Frazer Jarvis )

He presented NFS by working example(including factorbase construction on both Algebraic and Rational side and many other things).

But for FFS I searched a lot but didn't find any example and it is very difficult to grasp its concept by theory only. Please if anyone can refer or give working example of FFS, it will be very helpful.

  • $\begingroup$ The "give working example of FFS" part of this question (narrowly) saves it from being off-topic, IMHO. If there's debate on that, make it a meta topic. $\endgroup$ – fgrieu Nov 20 '16 at 18:09
  • $\begingroup$ @fgrieu should i post it on other website of StackExchange? $\endgroup$ – Tanmay Sharma Nov 21 '16 at 7:18
  • $\begingroup$ I can't think of a better website on StackExchange (or elsewhere). But you could improve the question to make it more clearly on-topic: emphasize asking how the Function Field Sieve method for Discrete Logarithm works, preferably mentioning at what point you are stuck in the description that you are using. De-emphasize asking for a reference, and try introducing concrete working example as a way to solve a specific issue, like choice of polynomials in the factor base for some parameters. $\endgroup$ – fgrieu Nov 21 '16 at 8:09
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    $\begingroup$ You may want to avoid completely working with functions to grasp the idea a bit better (basically the NFS and FFS shares a lot of the ideas used). For instance the article by A.Joux and R.Lercier "The Function Field Sieve in the Medium Prime Case" (iacr.org/archive/eurocrypt2006/40040255/40040255.pdf) provides a good insight of how the things work, while avoiding functions, in my opinion. $\endgroup$ – Lery Nov 21 '16 at 20:10

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