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drmike


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Re: Urgent !! Help needed .!
Posted: Feb 18, 2009 11:52 AM   in response to: Jaya_21 in response to: Jaya_21
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The lowest level. So the curve is at the lowest level, and so are it's coefficients. The points on the curve become the next level. The addition of points is a higher level of abstraction. When adding two points you get another point on the curve. But to do the addition, you must perform a lot of lower level math.

Polynomials are also used for error correction codes, like those used on DVD's (Reed-Solomon codes). So binary fields and polynomial math are widely used in engineering applications. The math is not that hard really, but it can be abstract. Keeping track of which math is doing what tends to get confusing, so I like to go slow and make sure I'm using binary fields, prime factors and point addition at the correct time.

Jaya_21

Posts: 39
Registered: 2/12/09
Re: Urgent !! Help needed .!
Posted: Feb 19, 2009 4:32 AM   in response to: drmike in response to: drmike
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Okay , Sir. Thnk U.

I would lik 2 kno about different variations of the ECDSA algorithm.
Can U pls explain them to me and provide me links for papers and materials about these variations ?

Thanks in advance ,
Jaya.

drmike


Posts: 543
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Re: Urgent !! Help needed .!
Posted: Feb 19, 2009 7:58 AM   in response to: Jaya_21 in response to: Jaya_21
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I describe two signature schemes in the book. But you can look here:
http://csrc.nist.gov/groups/ST/toolkit/digital_signatures.html
to find out what the present standard is in the USA.

For ECDSA there is only one method that is not patented, the NR scheme is. I'm not sure when that patent expires though, so it may be ok to use it now. Other than that, I don't know of any other elliptic curve versions.

Jaya_21

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Re: Urgent !! Help needed .!
Posted: Feb 19, 2009 12:21 PM   in response to: drmike in response to: drmike
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But Sir , is thr any chance of improvising the performance of the algorithm by making some changes in any of the steps (like scalar multiplication) ?

Right now I hav implemented the "Double and Add" method for scalar multiplication. Something more better Sir?

Can variations be thought about in this angle Sir?

Sir. . I hav successfully completed ECDSA Java implementation for NIST prime curves. What % of effort will be needed to convert the code to wrk well for binary B 163 curve? Really scared of this binary stuff. But we are asked in the college to come out with binary implementation also. :-(

Thnx in advance,
Jaya.

drmike


Posts: 543
Registered: 4/16/04
Re: Urgent !! Help needed .!
Posted: Feb 19, 2009 12:59 PM   in response to: Jaya_21 in response to: Jaya_21
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It's not that scary if you take your time and learn a few basics. The elliptic curve stuff is really deep, but you don't need to know as much as a professor of mathematics!

The main place to start is chapter 3. This was written for people who have no knowledge of this kind of math. My sons are learning polynomials in high school, I'm sure you have all the math you need. It is just learning how to apply it in a new way.

Relax - math is fun. Not scary! :-)

Jaya_21

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Registered: 2/12/09
Re: Urgent !! Help needed .!
Posted: Feb 20, 2009 1:55 AM   in response to: drmike in response to: drmike
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Sir,
I dont hav ur book. Whr do I get it ? Because , I dont hv a credit card I wil not b able to make online transactions also. :-(
Wil U pls get me the details of buying ur book , Sir ?

drmike


Posts: 543
Registered: 4/16/04
Re: Urgent !! Help needed .!
Posted: Feb 20, 2009 8:11 AM   in response to: Jaya_21 in response to: Jaya_21
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You will have to go to a local book store and order it. They can get it from an online store for you. There are many book stores online in India, I am certain there are many ways to get it! If you really want to learn this, it will be a good way to start.

Besides, you can find many other books online this way, and then have the local book store order it for you. If there is no local library, it is a way to make your own :-)

Jaya_21

Posts: 39
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Re: Urgent !! Help needed .!
Posted: Feb 20, 2009 12:17 PM   in response to: drmike in response to: drmike
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Yes , Sir.
I am trying to get the book. :-)
Thank U.

Jaya_21

Posts: 39
Registered: 2/12/09
Re: Urgent !! Help needed .!
Posted: Feb 24, 2009 12:26 PM   in response to: Jaya_21 in response to: Jaya_21
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Sir ,

I would like to know the different methods of implementing Scalar Multiplication.
Can U please direct me to some papers dealing with those different methods?

Thanks in advance,
Jaya.

drmike


Posts: 543
Registered: 4/16/04
Re: Urgent !! Help needed .!
Posted: Feb 24, 2009 12:46 PM   in response to: Jaya_21 in response to: Jaya_21
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I think you mean "modular multiplication". A web search on that will get you some good papers:
www.vlsi.informatik.tu-darmstadt.de/staff/laue/publications/crash2005_slides.pdf
and
http://www.informatica.si/PDF/30-1/10_Nedjah-A%20Review%20of%20Modular%20Multiplication%20Methods%20and...pdf
both look like good reviews.

Jaya_21

Posts: 39
Registered: 2/12/09
Re: Urgent !! Help needed .!
Posted: Feb 24, 2009 10:57 PM   in response to: drmike in response to: drmike
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Sir . . I donno what modular multiplication means.
Referred to the papers U had suggested.

I am asking about the different methods of doing kP (k , an integer and P, a point on the curve). This is what I meant as scalar multiplication, Sir.

For example , the Double and Add Method. I am asking for similar such methods Sir.

Sir . . then U had told me that there does not exist any variations as such for ECDSA algorithm. Okay , Sir.
How about improvisations suggested for the algorithm?

Thanks,
Jaya.

Message was edited by:
Jaya_21

drmike


Posts: 543
Registered: 4/16/04
Re: Urgent !! Help needed .!
Posted: Feb 25, 2009 8:12 AM   in response to: Jaya_21 in response to: Jaya_21
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OK, I see. I guess I call that "point multiplication". I describe a couple of methods in the book based on several papers of the time. But here is a recent paper you might find very interesting (I sure do!):
http://eprint.iacr.org/2008/390
"Elliptic Curve Cryptography: The Serpentine Course of a Paradigm Shift"

There are discussions about different digital signature schemes and multiplication methods.

Another good web page is this one: http://www.isg.rhul.ac.uk/~sdg/ecc.html
Look at Edwards curves for alternative methods that is more recent.

Jaya_21

Posts: 39
Registered: 2/12/09
Re: Urgent !! Help needed .!
Posted: Feb 25, 2009 11:38 AM   in response to: drmike in response to: drmike
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Okay Sir.

This question is not about ECC. But then I am putting it across U.


Sir. . If U remember , I had told U long back that our project is about smart cards.
We browsed and found the architecture of smart card , the PIC used , etc and all that Sir.

We are going to implement the ECDSA Signature Generation algorithm on the 16F874 processor. Basically V wil be running the algo on that processor.
Language used : Embedded C
IDE : MP Lab

My teacher here had asked to browse and check out as to how the security of the smart card can be improvised.
Now , how do we brinng in security ascepts here , Sir ?
How do we handle hardware and software attacks on the smart card?
How do we illstrate it in our project , Sir ?

Thanks in advance,
Jaya.

drmike


Posts: 543
Registered: 4/16/04
Re: Urgent !! Help needed .!
Posted: Feb 25, 2009 1:21 PM   in response to: Jaya_21 in response to: Jaya_21
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Here's some stuff you might want to look at:
http://www.springerlink.com/content/uj2cc95ultum7fwh/
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.1300
http://www.securitytechnet.com/crypto/algorithm/ecc.html
http://www.springerlink.com/content/eu1uqtk9g79fc14d/

and this guy is probably the leading expert in the world on the subject:
http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/p/Paar:Christof.html

Jaya_21

Posts: 39
Registered: 2/12/09
Re: Urgent !! Help needed .!
Posted: Feb 25, 2009 11:51 PM   in response to: drmike in response to: drmike
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Thanks a lot , Sir.

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