Can $sigma(n)$ be computed in polynomial time?
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If $sigma(n)$ is the sum of the divisors of $n$, can $sigma(n)$ be computed in the polynomial time no matter how large $n$ is?
If so, then by computing $sigma(n)$ and $phi(n)$, Euler totient function, using the discrete Fourier transform of the gcd evaluated at 1, one can easily get $p$ and $q$ such that $n=pq$ from:
from the link https://en.wikipedia.org/wiki/Divisor_function
And this should solve RSA encryption problem.
number-theory
asked Jan 19 at 19:36
isaacisaac
213
$endgroup$
add a comment |
$begingroup$
If $sigma(n)$ is the sum of the divisors of $n$, can $sigma(n)$ be computed in the polynomial time no matter how large $n$ is?
If so, then by computing $sigma(n)$ and $phi(n)$, Euler totient function, using the discrete Fourier transform of the gcd evaluated at 1, one can easily get $p$ and $q$ such that $n=pq$ from:
from the link https://en.wikipedia.org/wiki/Divisor_function
And this should solve RSA encryption problem.
number-theory
asked Jan 19 at 19:36
isaacisaac
213
$endgroup$
3
$begingroup$
Computing $sigma(n)$ is more or less equivalent to factorizing $n$, up to polynomial time. But the latter cannot be done in polynomial time. So the answer to the title question is "no".
$endgroup$
– Dietrich Burde
Jan 19 at 19:40
$begingroup$
@DietrichBurde You mean factoring $n$ in $log(n)$-polynomial time ?
$endgroup$
– reuns
Jan 20 at 2:49
add a comment |
$begingroup$
If $sigma(n)$ is the sum of the divisors of $n$, can $sigma(n)$ be computed in the polynomial time no matter how large $n$ is?
If so, then by computing $sigma(n)$ and $phi(n)$, Euler totient function, using the discrete Fourier transform of the gcd evaluated at 1, one can easily get $p$ and $q$ such that $n=pq$ from:
from the link https://en.wikipedia.org/wiki/Divisor_function
And this should solve RSA encryption problem.
number-theory
asked Jan 19 at 19:36
isaacisaac
213
$endgroup$
If $sigma(n)$ is the sum of the divisors of $n$, can $sigma(n)$ be computed in the polynomial time no matter how large $n$ is?
If so, then by computing $sigma(n)$ and $phi(n)$, Euler totient function, using the discrete Fourier transform of the gcd evaluated at 1, one can easily get $p$ and $q$ such that $n=pq$ from:
from the link https://en.wikipedia.org/wiki/Divisor_function
And this should solve RSA encryption problem.
number-theory
number-theory
asked Jan 19 at 19:36
isaacisaac
213
asked Jan 19 at 19:36
isaacisaac
213
asked Jan 19 at 19:36
isaacisaac
213
asked Jan 19 at 19:36
isaacisaac
213
asked Jan 19 at 19:36
isaacisaac
213
213
3
$begingroup$
Computing $sigma(n)$ is more or less equivalent to factorizing $n$, up to polynomial time. But the latter cannot be done in polynomial time. So the answer to the title question is "no".
$endgroup$
– Dietrich Burde
Jan 19 at 19:40
$begingroup$
@DietrichBurde You mean factoring $n$ in $log(n)$-polynomial time ?
$endgroup$
– reuns
Jan 20 at 2:49
add a comment |
3
$begingroup$
Computing $sigma(n)$ is more or less equivalent to factorizing $n$, up to polynomial time. But the latter cannot be done in polynomial time. So the answer to the title question is "no".
$endgroup$
– Dietrich Burde
Jan 19 at 19:40
$begingroup$
@DietrichBurde You mean factoring $n$ in $log(n)$-polynomial time ?
$endgroup$
– reuns
Jan 20 at 2:49
3
3
$begingroup$
Computing $sigma(n)$ is more or less equivalent to factorizing $n$, up to polynomial time. But the latter cannot be done in polynomial time. So the answer to the title question is "no".
$endgroup$
– Dietrich Burde
Jan 19 at 19:40
$begingroup$
Computing $sigma(n)$ is more or less equivalent to factorizing $n$, up to polynomial time. But the latter cannot be done in polynomial time. So the answer to the title question is "no".
$endgroup$
– Dietrich Burde
Jan 19 at 19:40
$begingroup$
@DietrichBurde You mean factoring $n$ in $log(n)$-polynomial time ?
$endgroup$
– reuns
Jan 20 at 2:49
$begingroup$
@DietrichBurde You mean factoring $n$ in $log(n)$-polynomial time ?
$endgroup$
– reuns
Jan 20 at 2:49
add a comment |
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$begingroup$
Computing $sigma(n)$ is more or less equivalent to factorizing $n$, up to polynomial time. But the latter cannot be done in polynomial time. So the answer to the title question is "no".
$endgroup$
– Dietrich Burde
Jan 19 at 19:40
$begingroup$
@DietrichBurde You mean factoring $n$ in $log(n)$-polynomial time ?
$endgroup$
– reuns
Jan 20 at 2:49