[*Note: Big thanks for Fajar Yuliawan for his brilliant tutorial 😉 ]
Tagged: elliptic curve Toggle Comment Threads | Keyboard Shortcuts
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
- The calculation starts from LSB
- Every bit shift means doubling, bit 1 means added by P and bit 0 means not added by P
- Adding costs more than doubling
Forgot to post an update about me shopping some books, really cool ones 🙂
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 😉
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 😉
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… ]
I guess now I start to grab the ideas about those previous paragraphs 🙂
I’ll check it to mathematician buddy as soon as possible 😉
chikaradirghsa, gre, and tetangga sebelah are discussing. Toggle Comments
- D. Hankerson, J.L. Hernandez, A. Menezes, “Software Implementation of Elliptic Curve Cryptography over Binary Fields”
- M. Brown, D. Hankerson, J. Lopez, A. Menezes, “Software Implementation of the NIST Elliptic Curves over Prime Fields”