Found $x^8$ while calculating inverse of $(x^6+1)$ in finite field $GF(2^8)$. Help???Quadratic Extension of Finite fieldInverse of polynomial over $mathbb F_3$ finite field, quotient spaceExtended Euclidean Algorithm, what is our answer?Calculating the generator of a Finite FieldIs every finite extension of a finite field a finite field?Algebraic Field Extension of Finite FieldPrescribing norm and trace of elements in a finite field.Help determining if a field is finite?degree of finite extension of finite fieldHelp with a basic question on Finite Field characteristic
In the late 1940’s to early 1950’s what technology was available that could melt a LOT of ice?
What Happens when Passenger Refuses to Fly Boeing 737 Max?
Replacing Windows 7 security updates with anti-virus?
Grey hair or white hair
Upside Down Word Puzzle
Is "history" a male-biased word ("his+story")?
How could our ancestors have domesticated a solitary predator?
If the Captain's screens are out, does he switch seats with the co-pilot?
How do I locate a classical quotation?
A question on the ultrafilter number
A three room house but a three headED dog
They call me Inspector Morse
Why does Captain Marvel assume the planet where she lands would recognize her credentials?
Are the terms "stab" and "staccato" synonyms?
Aliens englobed the Solar System: will we notice?
Why the color red for the Republican Party
Built-In Shelves/Bookcases - IKEA vs Built
Is having access to past exams cheating and, if yes, could it be proven just by a good grade?
How to create a hard link to an inode (ext4)?
Make a transparent 448*448 image
Peter's Strange Word
Finding algorithms of QGIS commands?
Why does the negative sign arise in this thermodynamic relation?
Making a sword in the stone, in a medieval world without magic
Found $x^8$ while calculating inverse of $(x^6+1)$ in finite field $GF(2^8)$. Help???
Quadratic Extension of Finite fieldInverse of polynomial over $mathbb F_3$ finite field, quotient spaceExtended Euclidean Algorithm, what is our answer?Calculating the generator of a Finite FieldIs every finite extension of a finite field a finite field?Algebraic Field Extension of Finite FieldPrescribing norm and trace of elements in a finite field.Help determining if a field is finite?degree of finite extension of finite fieldHelp with a basic question on Finite Field characteristic
$begingroup$
So I was running the EEA (Extended Euclidean Algorithm) to find the multiplicative inverse of $(x^6+1)$ in the finite field $GF(2^8)$. Everything was going fine until the second last iteration where I was supposed to get my $t(x)$ auxiliary polynomial that was going to be the inverse. However, this is what I got:
$$1=(x+1)-1(x)
=(r_1+x^2 r_0+x^4 r_1+xr_0+x^3 r_1)+x(x^5 r_0+x^4 r_0+x^3 r_0+x^2 r_0+r_0+x^7 r_1+x^6 r_1+x^5 r_1+x^4 r_1+x^3 r_1+x^2 r_1+xr_1)$$
This equated to $$(x^6+x^5+x^4+x^3+x^2 ) r_0+(x^8+x^7+x^6+x^5+x^3+1)r_1$$
But as much as I know, there shouldn't be a value greater than x^7 in the polynomial, should there? Please Help I need to submit an assignment day after tomorrow...
(EDIT)
enter image description here
This is an image of the EEA calculations
finite-fields extension-field euclidean-algorithm
New contributor
$endgroup$
|
show 2 more comments
$begingroup$
So I was running the EEA (Extended Euclidean Algorithm) to find the multiplicative inverse of $(x^6+1)$ in the finite field $GF(2^8)$. Everything was going fine until the second last iteration where I was supposed to get my $t(x)$ auxiliary polynomial that was going to be the inverse. However, this is what I got:
$$1=(x+1)-1(x)
=(r_1+x^2 r_0+x^4 r_1+xr_0+x^3 r_1)+x(x^5 r_0+x^4 r_0+x^3 r_0+x^2 r_0+r_0+x^7 r_1+x^6 r_1+x^5 r_1+x^4 r_1+x^3 r_1+x^2 r_1+xr_1)$$
This equated to $$(x^6+x^5+x^4+x^3+x^2 ) r_0+(x^8+x^7+x^6+x^5+x^3+1)r_1$$
But as much as I know, there shouldn't be a value greater than x^7 in the polynomial, should there? Please Help I need to submit an assignment day after tomorrow...
(EDIT)
enter image description here
This is an image of the EEA calculations
finite-fields extension-field euclidean-algorithm
New contributor
$endgroup$
1
$begingroup$
Please use MathJax to make your question readable. Start by putting$
signs around the math expressions.
$endgroup$
– saulspatz
2 days ago
$begingroup$
Changed it, sorry didnt realize that at first..
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Welcome to Maths SX! What is $x$ here?
$endgroup$
– Bernard
2 days ago
$begingroup$
x is just a variable, that shows the bit value in an 8-bit vector. So, for example, the polynomial $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ in bit value is (11111110)
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Btw in the look up table the inverse is actually equal to (11111110) meaning that the 4th iteration's $$r_1$$ is the correct answer
$endgroup$
– hassan zaidi
2 days ago
|
show 2 more comments
$begingroup$
So I was running the EEA (Extended Euclidean Algorithm) to find the multiplicative inverse of $(x^6+1)$ in the finite field $GF(2^8)$. Everything was going fine until the second last iteration where I was supposed to get my $t(x)$ auxiliary polynomial that was going to be the inverse. However, this is what I got:
$$1=(x+1)-1(x)
=(r_1+x^2 r_0+x^4 r_1+xr_0+x^3 r_1)+x(x^5 r_0+x^4 r_0+x^3 r_0+x^2 r_0+r_0+x^7 r_1+x^6 r_1+x^5 r_1+x^4 r_1+x^3 r_1+x^2 r_1+xr_1)$$
This equated to $$(x^6+x^5+x^4+x^3+x^2 ) r_0+(x^8+x^7+x^6+x^5+x^3+1)r_1$$
But as much as I know, there shouldn't be a value greater than x^7 in the polynomial, should there? Please Help I need to submit an assignment day after tomorrow...
(EDIT)
enter image description here
This is an image of the EEA calculations
finite-fields extension-field euclidean-algorithm
New contributor
$endgroup$
So I was running the EEA (Extended Euclidean Algorithm) to find the multiplicative inverse of $(x^6+1)$ in the finite field $GF(2^8)$. Everything was going fine until the second last iteration where I was supposed to get my $t(x)$ auxiliary polynomial that was going to be the inverse. However, this is what I got:
$$1=(x+1)-1(x)
=(r_1+x^2 r_0+x^4 r_1+xr_0+x^3 r_1)+x(x^5 r_0+x^4 r_0+x^3 r_0+x^2 r_0+r_0+x^7 r_1+x^6 r_1+x^5 r_1+x^4 r_1+x^3 r_1+x^2 r_1+xr_1)$$
This equated to $$(x^6+x^5+x^4+x^3+x^2 ) r_0+(x^8+x^7+x^6+x^5+x^3+1)r_1$$
But as much as I know, there shouldn't be a value greater than x^7 in the polynomial, should there? Please Help I need to submit an assignment day after tomorrow...
(EDIT)
enter image description here
This is an image of the EEA calculations
finite-fields extension-field euclidean-algorithm
finite-fields extension-field euclidean-algorithm
New contributor
New contributor
edited 2 days ago
hassan zaidi
New contributor
asked 2 days ago
hassan zaidihassan zaidi
11
11
New contributor
New contributor
1
$begingroup$
Please use MathJax to make your question readable. Start by putting$
signs around the math expressions.
$endgroup$
– saulspatz
2 days ago
$begingroup$
Changed it, sorry didnt realize that at first..
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Welcome to Maths SX! What is $x$ here?
$endgroup$
– Bernard
2 days ago
$begingroup$
x is just a variable, that shows the bit value in an 8-bit vector. So, for example, the polynomial $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ in bit value is (11111110)
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Btw in the look up table the inverse is actually equal to (11111110) meaning that the 4th iteration's $$r_1$$ is the correct answer
$endgroup$
– hassan zaidi
2 days ago
|
show 2 more comments
1
$begingroup$
Please use MathJax to make your question readable. Start by putting$
signs around the math expressions.
$endgroup$
– saulspatz
2 days ago
$begingroup$
Changed it, sorry didnt realize that at first..
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Welcome to Maths SX! What is $x$ here?
$endgroup$
– Bernard
2 days ago
$begingroup$
x is just a variable, that shows the bit value in an 8-bit vector. So, for example, the polynomial $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ in bit value is (11111110)
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Btw in the look up table the inverse is actually equal to (11111110) meaning that the 4th iteration's $$r_1$$ is the correct answer
$endgroup$
– hassan zaidi
2 days ago
1
1
$begingroup$
Please use MathJax to make your question readable. Start by putting
$
signs around the math expressions.$endgroup$
– saulspatz
2 days ago
$begingroup$
Please use MathJax to make your question readable. Start by putting
$
signs around the math expressions.$endgroup$
– saulspatz
2 days ago
$begingroup$
Changed it, sorry didnt realize that at first..
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Changed it, sorry didnt realize that at first..
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Welcome to Maths SX! What is $x$ here?
$endgroup$
– Bernard
2 days ago
$begingroup$
Welcome to Maths SX! What is $x$ here?
$endgroup$
– Bernard
2 days ago
$begingroup$
x is just a variable, that shows the bit value in an 8-bit vector. So, for example, the polynomial $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ in bit value is (11111110)
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
x is just a variable, that shows the bit value in an 8-bit vector. So, for example, the polynomial $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ in bit value is (11111110)
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Btw in the look up table the inverse is actually equal to (11111110) meaning that the 4th iteration's $$r_1$$ is the correct answer
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Btw in the look up table the inverse is actually equal to (11111110) meaning that the 4th iteration's $$r_1$$ is the correct answer
$endgroup$
– hassan zaidi
2 days ago
|
show 2 more comments
1 Answer
1
active
oldest
votes
$begingroup$
Judging from the calculation at the link you provided, you're taking $ x $ to be a root of the polynomial $ x^8 + x^4 + x^3 + x + 1 $. There's nothing particulary wrong about having terms of degree $8$ or more in an expression for the inverse of an element of the field, but you can always replace them with a combination of terms of smaller degree by using the equation $ x^8 = x^4 + x^3 + x + 1 $. As it happens, when I multiplied your putative inverse $ x^8+x^7+x^6+x^5+x^3+1= x^7+x^6+x^5+x^4+x $ by $ x^6+1 $ I didn't get $1$. I got $ x^5 $ instead.
In fact, there appears to be an error on line $2$ of the calculation pointed to by your link. I believe the remainder on the right side of the equation should be $ x^4 + x^3 +x^2 + x + 1 $ rather than $ x^4 + x^3 + x + 1 $.
$endgroup$
$begingroup$
Yes you are right there was a problem in line 2, however, it was only a mistake of not writing the $$x^2$$ and I'm saying that because I rechecked my calculation twice after you pointed it out. And yes you are right $$x^7+x^6+x^5+x^4+x$$ is not the correct inverse of $$x^6+1$$ the correct inverse I got from a look table was actually $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ . And I get it now that we can write the >8 terms using smaller degrees, but still, I don't quite understand why I'm not getting the correct answer. And btw this is of tremendous help.
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
I suggest you check your calculation of the coefficient of $ r_1 $ in the second column of line 5. According to my calculations this should be $ left(x^4+x^3+1right)left(x^3+xright) + x^2 $, which gives me a different result from what you have.
$endgroup$
– lonza leggiera
yesterday
$begingroup$
Guys this was extremely helpful and I'd like to thank everyone that commented. I realized my mistake, it was in the 5th iteration. The coefficient that was next to $$r_0$$ was written as $$x^8+x^7+x^6+x^5+x^3+1$$ when it was actually $$x^8+x^7+x^6+x^5+x^2+1$$. Thank you all for the comments.
$endgroup$
– hassan zaidi
yesterday
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
hassan zaidi is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3142227%2ffound-x8-while-calculating-inverse-of-x61-in-finite-field-gf28-he%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Judging from the calculation at the link you provided, you're taking $ x $ to be a root of the polynomial $ x^8 + x^4 + x^3 + x + 1 $. There's nothing particulary wrong about having terms of degree $8$ or more in an expression for the inverse of an element of the field, but you can always replace them with a combination of terms of smaller degree by using the equation $ x^8 = x^4 + x^3 + x + 1 $. As it happens, when I multiplied your putative inverse $ x^8+x^7+x^6+x^5+x^3+1= x^7+x^6+x^5+x^4+x $ by $ x^6+1 $ I didn't get $1$. I got $ x^5 $ instead.
In fact, there appears to be an error on line $2$ of the calculation pointed to by your link. I believe the remainder on the right side of the equation should be $ x^4 + x^3 +x^2 + x + 1 $ rather than $ x^4 + x^3 + x + 1 $.
$endgroup$
$begingroup$
Yes you are right there was a problem in line 2, however, it was only a mistake of not writing the $$x^2$$ and I'm saying that because I rechecked my calculation twice after you pointed it out. And yes you are right $$x^7+x^6+x^5+x^4+x$$ is not the correct inverse of $$x^6+1$$ the correct inverse I got from a look table was actually $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ . And I get it now that we can write the >8 terms using smaller degrees, but still, I don't quite understand why I'm not getting the correct answer. And btw this is of tremendous help.
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
I suggest you check your calculation of the coefficient of $ r_1 $ in the second column of line 5. According to my calculations this should be $ left(x^4+x^3+1right)left(x^3+xright) + x^2 $, which gives me a different result from what you have.
$endgroup$
– lonza leggiera
yesterday
$begingroup$
Guys this was extremely helpful and I'd like to thank everyone that commented. I realized my mistake, it was in the 5th iteration. The coefficient that was next to $$r_0$$ was written as $$x^8+x^7+x^6+x^5+x^3+1$$ when it was actually $$x^8+x^7+x^6+x^5+x^2+1$$. Thank you all for the comments.
$endgroup$
– hassan zaidi
yesterday
add a comment |
$begingroup$
Judging from the calculation at the link you provided, you're taking $ x $ to be a root of the polynomial $ x^8 + x^4 + x^3 + x + 1 $. There's nothing particulary wrong about having terms of degree $8$ or more in an expression for the inverse of an element of the field, but you can always replace them with a combination of terms of smaller degree by using the equation $ x^8 = x^4 + x^3 + x + 1 $. As it happens, when I multiplied your putative inverse $ x^8+x^7+x^6+x^5+x^3+1= x^7+x^6+x^5+x^4+x $ by $ x^6+1 $ I didn't get $1$. I got $ x^5 $ instead.
In fact, there appears to be an error on line $2$ of the calculation pointed to by your link. I believe the remainder on the right side of the equation should be $ x^4 + x^3 +x^2 + x + 1 $ rather than $ x^4 + x^3 + x + 1 $.
$endgroup$
$begingroup$
Yes you are right there was a problem in line 2, however, it was only a mistake of not writing the $$x^2$$ and I'm saying that because I rechecked my calculation twice after you pointed it out. And yes you are right $$x^7+x^6+x^5+x^4+x$$ is not the correct inverse of $$x^6+1$$ the correct inverse I got from a look table was actually $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ . And I get it now that we can write the >8 terms using smaller degrees, but still, I don't quite understand why I'm not getting the correct answer. And btw this is of tremendous help.
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
I suggest you check your calculation of the coefficient of $ r_1 $ in the second column of line 5. According to my calculations this should be $ left(x^4+x^3+1right)left(x^3+xright) + x^2 $, which gives me a different result from what you have.
$endgroup$
– lonza leggiera
yesterday
$begingroup$
Guys this was extremely helpful and I'd like to thank everyone that commented. I realized my mistake, it was in the 5th iteration. The coefficient that was next to $$r_0$$ was written as $$x^8+x^7+x^6+x^5+x^3+1$$ when it was actually $$x^8+x^7+x^6+x^5+x^2+1$$. Thank you all for the comments.
$endgroup$
– hassan zaidi
yesterday
add a comment |
$begingroup$
Judging from the calculation at the link you provided, you're taking $ x $ to be a root of the polynomial $ x^8 + x^4 + x^3 + x + 1 $. There's nothing particulary wrong about having terms of degree $8$ or more in an expression for the inverse of an element of the field, but you can always replace them with a combination of terms of smaller degree by using the equation $ x^8 = x^4 + x^3 + x + 1 $. As it happens, when I multiplied your putative inverse $ x^8+x^7+x^6+x^5+x^3+1= x^7+x^6+x^5+x^4+x $ by $ x^6+1 $ I didn't get $1$. I got $ x^5 $ instead.
In fact, there appears to be an error on line $2$ of the calculation pointed to by your link. I believe the remainder on the right side of the equation should be $ x^4 + x^3 +x^2 + x + 1 $ rather than $ x^4 + x^3 + x + 1 $.
$endgroup$
Judging from the calculation at the link you provided, you're taking $ x $ to be a root of the polynomial $ x^8 + x^4 + x^3 + x + 1 $. There's nothing particulary wrong about having terms of degree $8$ or more in an expression for the inverse of an element of the field, but you can always replace them with a combination of terms of smaller degree by using the equation $ x^8 = x^4 + x^3 + x + 1 $. As it happens, when I multiplied your putative inverse $ x^8+x^7+x^6+x^5+x^3+1= x^7+x^6+x^5+x^4+x $ by $ x^6+1 $ I didn't get $1$. I got $ x^5 $ instead.
In fact, there appears to be an error on line $2$ of the calculation pointed to by your link. I believe the remainder on the right side of the equation should be $ x^4 + x^3 +x^2 + x + 1 $ rather than $ x^4 + x^3 + x + 1 $.
edited 2 days ago
answered 2 days ago
lonza leggieralonza leggiera
1,03228
1,03228
$begingroup$
Yes you are right there was a problem in line 2, however, it was only a mistake of not writing the $$x^2$$ and I'm saying that because I rechecked my calculation twice after you pointed it out. And yes you are right $$x^7+x^6+x^5+x^4+x$$ is not the correct inverse of $$x^6+1$$ the correct inverse I got from a look table was actually $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ . And I get it now that we can write the >8 terms using smaller degrees, but still, I don't quite understand why I'm not getting the correct answer. And btw this is of tremendous help.
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
I suggest you check your calculation of the coefficient of $ r_1 $ in the second column of line 5. According to my calculations this should be $ left(x^4+x^3+1right)left(x^3+xright) + x^2 $, which gives me a different result from what you have.
$endgroup$
– lonza leggiera
yesterday
$begingroup$
Guys this was extremely helpful and I'd like to thank everyone that commented. I realized my mistake, it was in the 5th iteration. The coefficient that was next to $$r_0$$ was written as $$x^8+x^7+x^6+x^5+x^3+1$$ when it was actually $$x^8+x^7+x^6+x^5+x^2+1$$. Thank you all for the comments.
$endgroup$
– hassan zaidi
yesterday
add a comment |
$begingroup$
Yes you are right there was a problem in line 2, however, it was only a mistake of not writing the $$x^2$$ and I'm saying that because I rechecked my calculation twice after you pointed it out. And yes you are right $$x^7+x^6+x^5+x^4+x$$ is not the correct inverse of $$x^6+1$$ the correct inverse I got from a look table was actually $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ . And I get it now that we can write the >8 terms using smaller degrees, but still, I don't quite understand why I'm not getting the correct answer. And btw this is of tremendous help.
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
I suggest you check your calculation of the coefficient of $ r_1 $ in the second column of line 5. According to my calculations this should be $ left(x^4+x^3+1right)left(x^3+xright) + x^2 $, which gives me a different result from what you have.
$endgroup$
– lonza leggiera
yesterday
$begingroup$
Guys this was extremely helpful and I'd like to thank everyone that commented. I realized my mistake, it was in the 5th iteration. The coefficient that was next to $$r_0$$ was written as $$x^8+x^7+x^6+x^5+x^3+1$$ when it was actually $$x^8+x^7+x^6+x^5+x^2+1$$. Thank you all for the comments.
$endgroup$
– hassan zaidi
yesterday
$begingroup$
Yes you are right there was a problem in line 2, however, it was only a mistake of not writing the $$x^2$$ and I'm saying that because I rechecked my calculation twice after you pointed it out. And yes you are right $$x^7+x^6+x^5+x^4+x$$ is not the correct inverse of $$x^6+1$$ the correct inverse I got from a look table was actually $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ . And I get it now that we can write the >8 terms using smaller degrees, but still, I don't quite understand why I'm not getting the correct answer. And btw this is of tremendous help.
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Yes you are right there was a problem in line 2, however, it was only a mistake of not writing the $$x^2$$ and I'm saying that because I rechecked my calculation twice after you pointed it out. And yes you are right $$x^7+x^6+x^5+x^4+x$$ is not the correct inverse of $$x^6+1$$ the correct inverse I got from a look table was actually $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ . And I get it now that we can write the >8 terms using smaller degrees, but still, I don't quite understand why I'm not getting the correct answer. And btw this is of tremendous help.
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
I suggest you check your calculation of the coefficient of $ r_1 $ in the second column of line 5. According to my calculations this should be $ left(x^4+x^3+1right)left(x^3+xright) + x^2 $, which gives me a different result from what you have.
$endgroup$
– lonza leggiera
yesterday
$begingroup$
I suggest you check your calculation of the coefficient of $ r_1 $ in the second column of line 5. According to my calculations this should be $ left(x^4+x^3+1right)left(x^3+xright) + x^2 $, which gives me a different result from what you have.
$endgroup$
– lonza leggiera
yesterday
$begingroup$
Guys this was extremely helpful and I'd like to thank everyone that commented. I realized my mistake, it was in the 5th iteration. The coefficient that was next to $$r_0$$ was written as $$x^8+x^7+x^6+x^5+x^3+1$$ when it was actually $$x^8+x^7+x^6+x^5+x^2+1$$. Thank you all for the comments.
$endgroup$
– hassan zaidi
yesterday
$begingroup$
Guys this was extremely helpful and I'd like to thank everyone that commented. I realized my mistake, it was in the 5th iteration. The coefficient that was next to $$r_0$$ was written as $$x^8+x^7+x^6+x^5+x^3+1$$ when it was actually $$x^8+x^7+x^6+x^5+x^2+1$$. Thank you all for the comments.
$endgroup$
– hassan zaidi
yesterday
add a comment |
hassan zaidi is a new contributor. Be nice, and check out our Code of Conduct.
hassan zaidi is a new contributor. Be nice, and check out our Code of Conduct.
hassan zaidi is a new contributor. Be nice, and check out our Code of Conduct.
hassan zaidi is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3142227%2ffound-x8-while-calculating-inverse-of-x61-in-finite-field-gf28-he%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
Please use MathJax to make your question readable. Start by putting
$
signs around the math expressions.$endgroup$
– saulspatz
2 days ago
$begingroup$
Changed it, sorry didnt realize that at first..
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Welcome to Maths SX! What is $x$ here?
$endgroup$
– Bernard
2 days ago
$begingroup$
x is just a variable, that shows the bit value in an 8-bit vector. So, for example, the polynomial $$x^7+x^6+x^5+x^4+x^3+x^2+x$$ in bit value is (11111110)
$endgroup$
– hassan zaidi
2 days ago
$begingroup$
Btw in the look up table the inverse is actually equal to (11111110) meaning that the 4th iteration's $$r_1$$ is the correct answer
$endgroup$
– hassan zaidi
2 days ago