Mixing
Understand an algorithm to find a prime of bit length $k$
$begingroup$
My cryptography notes gives this algorithm for finding a prime of bit-length larger than or equal to $k$.
- Determine an optimal bound on the set of small primes to be sieved
$(2,3,...,p_t)$ and let $M=(2)(3)...p_t$. - Generate a random integer $x$ whose bitlength is $k$ and locate, using the Chinese Remainder theorem, the smallest integer $x_1$ larger than $x$ which is co-prime to $M$.
- Perform an incremental search for primes in the set $x_1, x_1+M, x_1+2M$.
I have two questions
How do you find the smallest integer $x_1>x$ using the Chinese remainder theorem that is co-prime to $M$.
Why is it true that any of the integers in $(x_1, x_1+M$) are sieved. How do we know none of them are primes?
Thanks.
cryptography
asked Jan 26 at 22:07
IntegrateThisIntegrateThis
1,9441818
$endgroup$
add a comment |
$begingroup$
My cryptography notes gives this algorithm for finding a prime of bit-length larger than or equal to $k$.
- Determine an optimal bound on the set of small primes to be sieved
$(2,3,...,p_t)$ and let $M=(2)(3)...p_t$. - Generate a random integer $x$ whose bitlength is $k$ and locate, using the Chinese Remainder theorem, the smallest integer $x_1$ larger than $x$ which is co-prime to $M$.
- Perform an incremental search for primes in the set $x_1, x_1+M, x_1+2M$.
I have two questions
How do you find the smallest integer $x_1>x$ using the Chinese remainder theorem that is co-prime to $M$.
Why is it true that any of the integers in $(x_1, x_1+M$) are sieved. How do we know none of them are primes?
Thanks.
cryptography
asked Jan 26 at 22:07
IntegrateThisIntegrateThis
1,9441818
$endgroup$
add a comment |
$begingroup$
My cryptography notes gives this algorithm for finding a prime of bit-length larger than or equal to $k$.
- Determine an optimal bound on the set of small primes to be sieved
$(2,3,...,p_t)$ and let $M=(2)(3)...p_t$. - Generate a random integer $x$ whose bitlength is $k$ and locate, using the Chinese Remainder theorem, the smallest integer $x_1$ larger than $x$ which is co-prime to $M$.
- Perform an incremental search for primes in the set $x_1, x_1+M, x_1+2M$.
I have two questions
How do you find the smallest integer $x_1>x$ using the Chinese remainder theorem that is co-prime to $M$.
Why is it true that any of the integers in $(x_1, x_1+M$) are sieved. How do we know none of them are primes?
Thanks.
cryptography
asked Jan 26 at 22:07
IntegrateThisIntegrateThis
1,9441818
$endgroup$
My cryptography notes gives this algorithm for finding a prime of bit-length larger than or equal to $k$.
- Determine an optimal bound on the set of small primes to be sieved
$(2,3,...,p_t)$ and let $M=(2)(3)...p_t$. - Generate a random integer $x$ whose bitlength is $k$ and locate, using the Chinese Remainder theorem, the smallest integer $x_1$ larger than $x$ which is co-prime to $M$.
- Perform an incremental search for primes in the set $x_1, x_1+M, x_1+2M$.
I have two questions
How do you find the smallest integer $x_1>x$ using the Chinese remainder theorem that is co-prime to $M$.
Why is it true that any of the integers in $(x_1, x_1+M$) are sieved. How do we know none of them are primes?
Thanks.
cryptography
cryptography
asked Jan 26 at 22:07
IntegrateThisIntegrateThis
1,9441818
asked Jan 26 at 22:07
IntegrateThisIntegrateThis
1,9441818
asked Jan 26 at 22:07
IntegrateThisIntegrateThis
1,9441818
asked Jan 26 at 22:07
IntegrateThisIntegrateThis
1,9441818
asked Jan 26 at 22:07
IntegrateThisIntegrateThis
1,9441818
1,9441818
add a comment |
add a comment |
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