• #### CG 9:25 pm on August 31, 2010 Permalink | Reply Tags: hardware implementation, PB ( 2 )

Need to find out if PB implementation in hw is good enough. Is ONB still better in hw for composite field?

• #### CG 10:52 pm on August 31, 2010 Permalink | Reply

kok bisa ya ada Type II Optimal Polynomial Bases?

• #### Xanax 4:01 am on April 21, 2013 Permalink | Reply

Your current report offers verified useful to me.

It’s very educational and you are clearly really well-informed in this field.

You possess popped my own face to be able to various opinion
of this specific topic together with intriquing, notable and solid
written content.

## To do, to think about. To keep the brain boiled.

1. PB or ONB?
2. Reducing polynomial
3. LUT in vhdl
4. Inverse algorithm
5. Mastrovito’s reduction matrix

## BlueKrypt – Cryptographic Key Length Recommendation

A brilliant web site that can quickly evaluate the level of security from keylength. Awesome.

• #### lia 1:01 pm on September 1, 2010 Permalink | Reply

panjang kunci aja kah…??
kalau pertimbangan/aspek lainnya.., trutama utk kriptografi asimetrik.,rekomendasinya apa yaa..?

• #### Budi Rahardjo 12:47 pm on August 27, 2010 Permalink | Reply

langsung di-refer di paper ah … 😀

• #### CG 4:06 pm on August 29, 2010 Permalink | Reply

cari reference dan masukkin ke bibdesk itu satu urusan sendiri 😀 gimana lagi kalau gak pake lyx ya? 😀

## Research discussion

Have just started regular discussion with mathematicians, and got a big boost on the research. I have read umpteen papers and produce nothing, while those math wizards took a glance at them and answer all my questions right away. Well, disconnected from them is a nightmare. Looking forward for discussion next week, now I have to decide Karatsuba Ofman or Mastrovito while coding vhdl for lookup table.

• #### Cyclops 11:13 pm on May 9, 2011 Permalink | Reply

Have you implemented the Mastrovito Multiplier in Verilog!? I’m a 4th year CSE student from IIT Kharagpur, and am researching on this presently. I would be grateful if you can mail me the code at rishav.mishraa@gmail.com

• #### CG 9:30 am on May 10, 2011 Permalink | Reply

we implemented it only in VHDL, have you read this book http://arithmetic-circuits.org/finite-field/index.html? it contains mastrovito multiplier in two versions, maybe you can reconstruct verilog version by looking at the downloable vhdl version.

• #### CG 9:13 pm on August 22, 2010 Permalink | Reply Tags: multiplier ( 11 ), ONB2 ( 4 )

Finished reading about multiplier over $GF(2^n)$ – polynomial bases.
Now moving on to multiplier for Optimal Normal Basis Type II.
1. An Efficient Optimal Normal Basis Type II Multiplier, B. Sunar, C. K. Koc
2. Brief Contributions – An Efficient Optimal Normal Basis Type II Multiplier, B. Sunar, C. K. Koc

Next will be designing multiplier for composite field and implement it in vhdl.

• #### Fernando Urbano 10:09 pm on November 7, 2010 Permalink | Reply

Greetings, I tried to implemented these multiplier for 233 bits, a Type II ONB, but I hadn’t success. Could you did it? If so, could you tell me how? Thanks!!!! Very nice blog I like it a lot of.

• #### CG 5:25 am on November 8, 2010 Permalink | Reply

hello fernando, thx for visiting the blog. i’m now still trying to implement multiplier for 299bits, using PB. maybe after successfully implement PB version (assuming that it’s easier than ONB II) then i will start using Type II ONB.

do you implement it using vhdl too?

• #### Fernando Urbano 12:00 pm on November 8, 2010 Permalink | Reply

yes, I did. But I think that something ws wrong with the permutage stage (changing base) to reconvert the result at the ONB again. I think that is very large multiplier compare with others. What kind of PB muliplier are you trying to implement?

• #### CG 12:13 pm on November 8, 2010 Permalink | Reply

we have developed conversion algorithm from PB – ONB1 and vice versa but not yet for PB – ONB2. what is your consideration of using ONB2? i’m trying to implement the two-step classic multiplication. i need a classic multiplication method to be compared to multiplication for composite field in PB representation. do you have any experiences with composite field?

• #### Fernando Urbano 11:37 pm on November 12, 2010 Permalink | Reply

We considere, OB2 because it’s the only one in these base from the five (m = 163, 233, 283, 409, 571) recommended by NIST for elliptic curve digital signature algorithm.

• #### CG 6:48 am on November 13, 2010 Permalink | Reply

oh i see. you’re referring NIST for choosing the curve. have you published any papers related to what you’re working on now? i’d like to read if there’s any 🙂 thx

• #### CG 4:56 pm on August 21, 2010 Permalink | Reply Tags: finite fields ( 9 ), hardware ( 19 ), multiplier ( 11 ), vhdl ( 45 )

Hardware Implementation of Finite-Field Arithmetic – Jean Pierre Deschamps, Jose Luis Imana, Gustavo D. Sutter, Chapter 7.

Going to learn about all multiplier for finite fields. And think how can a non-finite field multiplier be applied for finite field applications.

• #### CG 11:01 am on August 20, 2010 Permalink | Reply Tags: composite field ( 16 ), finite fields ( 9 ), massey omura

1. Efficient Normal Basis Multipliers in Composite Fields – Sangho Oh, Chang Han Kim, Jongin Lim, and Dong Hyeon Cheon
2. Modular Construction of Low Complexity Parallel Multipliers for a Class of Finite Fields $GF(2^n)$ – M. A. Hasan, M. Z. Wang and V. K. Bhargava
3. A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields – M. A. Hasan, M. Z. Wang and V. K. Bhargava

## Choosing n and m for composite field

Referring to “Efficient Normal Basis Multipliers in Composite Fields” – Sangho Oh, Chang Han Kim, Jongin Lim, and Dong Hyeon Cheon, there is classification of hardware-applicable composite fields:

1. Type I composite field where a subfield $GF(2^n)$ in ONB2 and an extension field $GF(2^{nm})$ in ONB1
2. Type II composite field where a subfield $GF(2^n)$ in ONB1 and an extension field $GF(2^{nm})$ in ONB2
3. Type III composite field where a subfield $GF(2^n)$ in ONB2 and an extension field $GF(2^{nm})$ in ONB2

This is different with composite fields presented in “Efficient Methods for Composite Field Arithmetic” – E. Sava ̧s and C ̧. K. Koc, where the selection of $n$ and $m$  does not put their normal basis types (ONB1 or ONB2) into consideration.

Now the questions are:

1. Would it be better if we choose $n$, $m$ and $nm$ in ONB1/ONB2?
2. Which polynomial irreducible to be used? With degree = $n$, or degree = $m$ or degree = $nm$?

[pounding headache, and without answering these questions i wouldnt be able to start the hw design.]

## Snow Leopard: running in 32 or 64 bit?

Have just upgraded memory to 4GB and just found out that the Intel Core 2 Duo is 64 bit, I want to know whether my system running in 32 or 64 bit.

By default Snow Leopard run in 32 bit but can be changed to 64 by hitting “6” and “4” while booting. This is the result before:

After I boot and hold “6” and “4” keys, nothing’s changed. Why?
Because the EFI is still 32-bit, so my system cannot run 64-bit kernel. Oh well.

• #### Budi Rahardjo 2:52 pm on August 19, 2010 Permalink | Reply

apa ya untungnya upgrade ke 64-bit?

• #### CG 3:05 pm on August 19, 2010 Permalink | Reply

c
Compose new post
j
Next post/Next comment
k
Previous post/Previous comment
r
e
Edit
o
t
Go to top
l
h
Show/Hide help
shift + esc
Cancel