Drawing Elliptic Curve with Geometer Sketchpad
[*Note: Big thanks for Fajar Yuliawan for his brilliant tutorial π ]
[*Note: Big thanks for Fajar Yuliawan for his brilliant tutorial π ]
A Low-Power VHDL Design for an Elliptic Curve Digital Signature Chip – Richard Schroeppel, Cheryl Beaver, and Timothy Draelos – Cryptography and Information Systems Surety Department, September 2002
Notes:
to be frankly, i cannot see the pattern from the table.
i have different notation in my head π which is basically similar to what you wrote in your notes.
@BR: should there be any pattern anyway? π i’m so lost in multiplication of different bases π show me your notation π
Forgot to post an update about me shopping some books, really cool ones π
1. The “bible” of ECC: “Guide to Elliptic Curve Cryptography” – Darrel Hankerson, Alfred Menezes, Scott Vanstone
2. A very detail and theoritical book about elliptic curves: “Elliptic Curves – Number Theory and Cryptography” – Lawrence C. Washington
3. The most related book to be the reference of my phd thesis: “Elliptic Curve Cryptography for Constrained Devices – Algorithms, Architectures and Practical Implementations” – Sandeep S. Kumar
Happy holiday, everybody.
I’m going to spend the holiday with my new buddies π
Waaahhh … iri …
Buku baru selalu membuat iri π
@BR: hey, you’ve got to read them too and help me to understand and finish my phd π
the first one is a “bible” ?
hmmmm, oke, a must have ECC book isn’t, it.
I was going to observe the “behaviour” of an elliptic curve by changing its generator, and looking for an answer what does happen if I change it.
From the discussion yesterday, I understand that each generator will generate different cyclic subgroups. And does it have something to do with security level? Let’s find out.
Still thinking about changing other parameters of elliptic curve, and observe the result.
Eh, there are still some questions left, and I’m posting it here to remind me that I have to move forward from this point π
Question:
Why finite fields? Does it has something to do with “reversible”? Is that a requirement for only elliptic curve? Is it possible for elliptic curve without finite fields?
Multiplication over elliptic curve is like this:
where and are points on an elliptic curve and is an integer. The equation above means that is added to itself times.
What I don’t understand (yet) is, why the integer need not be larger than the “order” of the point ? Understand that reducing will save a great deal of processing. But what’s the relation between the “order” of the point with this statement:
The points in elliptic curve, forms a cyclic group (a field)
??? [back to reading… ]
Update:
I guess now I start to grab the ideas about those previous paragraphs π
I’ll check it to mathematician buddy as soon as possible π
walah baca postingan ini jadi merasa orang garut……dodol
cing atuh……pake bahasa manusia kalau posting tehhhh
@tetangga sebelah: cing atuh karunya ka sayah. lebaran mudik teh bawain oleh2x atuh, opor kek, dodol kek…
emang bukan bahasa manusia makanya saya juga ga ngarti…
speaking of field, you must be a knowledgeable person in abstract algebra and it is rarely found in LABTEK VIII π
I am just wondering if the k integer might be a Lipshitz constant.
@gre: not yet a knowledgeable person in abstract algebra π
what is a Lipshitz constant anyway? [pls don’t give more headaches to me now π ]
Now reading
Good! Summary, please.
Also, don’t forget to enter this into you bibliography database.
@BR: summary is in progress. already added to the bibliography database.
after the summary can you make a presentation in our ecc-study group about this book, please?
@intan: those are papers, not books. would be glad to give presentation, but need some time to prepare it. is 2 weeks from now ok? π
Budi Rahardjo 2:39 pm on November 4, 2011 Permalink |
yay! good stuff …