Finding working modulus for FFT over finite fields
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
I would like to implement multiplication of polynomials using NTT. I followed Number-theoretic transform (integer DFT) and it seems to work.
Now I would like to implement multiplication of polynomials over finite fields $mathbbZ_p[x]$ where $p$ is arbitrary prime number.
Does it changes anything that the coefficients are now bounded by $p$, compared to the former unbounded case?
In particular, original NTT required to find prime number $N$ as the working modulus that is larger than $(magnitude of largest element of input vector)^2 times (length of input vector) + 1$ so that the result never overflows. If the result is going to be bounded by modulo that $p$ prime anyway, how small can the modulus be? Note that $p - 1$ does not have to be of form $(some positive integer) * (length of input vector)$.
number-theory finite-fields convolution fast-fourier-transform
add a comment |Â
up vote
1
down vote
favorite
I would like to implement multiplication of polynomials using NTT. I followed Number-theoretic transform (integer DFT) and it seems to work.
Now I would like to implement multiplication of polynomials over finite fields $mathbbZ_p[x]$ where $p$ is arbitrary prime number.
Does it changes anything that the coefficients are now bounded by $p$, compared to the former unbounded case?
In particular, original NTT required to find prime number $N$ as the working modulus that is larger than $(magnitude of largest element of input vector)^2 times (length of input vector) + 1$ so that the result never overflows. If the result is going to be bounded by modulo that $p$ prime anyway, how small can the modulus be? Note that $p - 1$ does not have to be of form $(some positive integer) * (length of input vector)$.
number-theory finite-fields convolution fast-fourier-transform
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I would like to implement multiplication of polynomials using NTT. I followed Number-theoretic transform (integer DFT) and it seems to work.
Now I would like to implement multiplication of polynomials over finite fields $mathbbZ_p[x]$ where $p$ is arbitrary prime number.
Does it changes anything that the coefficients are now bounded by $p$, compared to the former unbounded case?
In particular, original NTT required to find prime number $N$ as the working modulus that is larger than $(magnitude of largest element of input vector)^2 times (length of input vector) + 1$ so that the result never overflows. If the result is going to be bounded by modulo that $p$ prime anyway, how small can the modulus be? Note that $p - 1$ does not have to be of form $(some positive integer) * (length of input vector)$.
number-theory finite-fields convolution fast-fourier-transform
I would like to implement multiplication of polynomials using NTT. I followed Number-theoretic transform (integer DFT) and it seems to work.
Now I would like to implement multiplication of polynomials over finite fields $mathbbZ_p[x]$ where $p$ is arbitrary prime number.
Does it changes anything that the coefficients are now bounded by $p$, compared to the former unbounded case?
In particular, original NTT required to find prime number $N$ as the working modulus that is larger than $(magnitude of largest element of input vector)^2 times (length of input vector) + 1$ so that the result never overflows. If the result is going to be bounded by modulo that $p$ prime anyway, how small can the modulus be? Note that $p - 1$ does not have to be of form $(some positive integer) * (length of input vector)$.
number-theory finite-fields convolution fast-fourier-transform
number-theory finite-fields convolution fast-fourier-transform
asked Sep 10 at 18:24
minmax
2159
2159
add a comment |Â
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
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
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2912201%2ffinding-working-modulus-for-fft-over-finite-fields%23new-answer', 'question_page');
);
Post as a guest
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
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
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