Talk:Finite field arithmetic

Rijndael Galois field

Great minds think alike; I independently wrote almost the same material for Rijndael Galois field. Can you say merge? Samboy 10:59, 29 May 2005 (UTC)[reply]

Copyvio

Someone may observe that the material here bears a striking resemblence to some material on my web page. This is because I am allowing the relevant materal on that web page to be released under the GFDL license; there is no copyright violation going on. Keep in mind that I myself can place material form my web page in to articles; however if anyone else copies materials form my web page in to articles, it is a Copyvio. Samboy 20:24, 29 May 2005 (UTC)[reply]

what?

By making a logarithm table of the finite field, and performing subtraction in the table. Subtraction of logarithms is the same as division.

this sounds like a brute force attack by an other name, am I wrong?

ADDED BY Paul NO. LOG(A) - LOG(B) = LOG(A/B) Meaning: A/B = EXP(LOG(A) - LOG(B)) Hence factor may be calculated as substraction of LOGs

Matrix Inversion Example

Can any one help me in finding the multiplicative inverse of ${\begin{bmatrix}1&0\\1&2\end{bmatrix}}$ in $GF(2^{4})$ step-by-step?

Small oops

I noticed a small oops in the text: > 0x1b corresponds to the irreducible polynomial x8 + x4 + x3 + x + 1.

0x1b is x^4 + x^3 + x + 1. 0x11b (as mentioned int he original Rijndael texts) is the actual polynomial. Since the bit you left off is the x^8 bit it's pointless to add it, but the text itself is still incorrect.

Added by Paul: Yes, this is absolutely pathetic. 0x1b cannot be "x^8 + x^4 + x^3 + x + 1" because "x^8 + x^4 + x^3 + x + 1" was the polynomial that we used for generation of the field. "x^8 + x^4 + x^3 + x + 1" = 0.

Sum of all field elements

Please see Talk:Field (mathematics)#Sum of all field elements. —The preceding unsigned comment was added by 80.178.241.65 (talk) 20:27, 15 April 2007 (UTC).[reply]

Inadequate description of algorithm

The description of the multiplication is really weird (the description, not the algorithm). It would be easier to understand in pseudocode than in natural language:

"an eight-bit product p": this is not clear, you should say that the product will be computed in a variable called $p$ ;
"make a copy of a and b...": this is a call to a function with parameter $a$ and $b$ ;

etc., every line would be smaller and more meaningful in pseudocode. I cannot understand why someone would write an algorithm in pure natural language. —The preceding unsigned comment was added by 81.247.15.55 (talk) 17:15, 9 May 2007 (UTC).[reply]

Long division edit?

Should there be something else instead of
0100011010
^000000000
in the middle of the long division example? Like the divisor 100011011
Sohannin (talk) 19:19, 30 March 2008 (UTC)[reply]

Inversion

I would like to add another method of doing inversion. I attempted it a while ago, but it was for the specific case of a 2⁸ field, not the general case. In a 2⁸ field, you can calculate an inverse by calculating x²⁵⁴. Due to being a finite field, x²⁵⁴ is equivalent to x^-1. Calculating x²⁵⁴ can be done using e.g. exponentiation by squaring. (Inefficient, but useful for example in an embedded processor where small code size is more important than speed.) Anyway, I've described the specific case here. What is the general method for any finite field? Cmcqueen1975 (talk) 01:08, 24 October 2008 (UTC)[reply]

vulnerable to timing attacks?

Under "Program Examples" after the sample code it says: "Note that this code is vulnerable to timing attacks when used for cryptography." However, this code has nothing to do with timing. Remove that warning?

SmilingRob (talk) 11:41, 8 February 2009 (UTC)[reply]

The article is focused on cryptography, and the code given is vulnerable to a cryptographic technique called a timing attack. The warning is therefore relevant. JackSchmidt (talk) 20:55, 8 February 2009 (UTC)[reply]

Zech logarithm

Thsi article is too mushy. Needs tautening. Where is the Zech logarithm? Lam & McKay collected algorithms ACM No 469. 96.21.220.144 (talk) 15:18, 11 March 2010 (UTC)John McKay[reply]

Arithmetic over a finite field

The Zech logarithm needs publicity! See Collected algorithms Lam & McKay Algorithm 469, Comm. ACM, vol. 15, 699, (1973)

Finite fields are mathematics. Cryptography is an application.

96.21.220.144 (talk) 15:16, 11 March 2010 (UTC)John McKay[reply]