Can integer factorization be solved in polynomial time on a classical computer?

Yes, a quantum computer can run a classical (meaning “non-quantum”) algorithm with polynomial run time in polynomial time.

Can factoring be done in polynomial time?

Difficulty and complexity No algorithm has been published that can factor all integers in polynomial time, that is, that can factor a b-bit number n in time O(bk) for some constant k.

Is integer factoring NP hard?

No. Integer factorization is not NP-hard (so not NP-complete). (This isn’t proven, but it’s generally thought to be the case.) So, while doing a polynomial-time integer factorization would be hugely significant (and make all asymmetric encryption in the world useless), it would not prove P=NP.

What is integer factorization in cryptography?

Prime Factorization (or integer factorization) is a commonly used mathematical problem often used to secure public-key encryption systems. A common practice is to use very large semi-primes (that is, the result of the multiplication of two prime numbers) as the number securing the encryption.

How fast is Shors algorithm?

A little math example shows why Shor’s algorithm is so effective. Suppose that if n is the quantity of digits in a number, Shor’s algorithm can factor that number in n10 seconds. So a two-digit number would take 210, or 1,024 seconds. A three-digit number would take 59,049 seconds, and so on.

Is integer factorization in P?

Integer factoring with the numbers represented in binary is (as far as we know) not in P.

Do factors have to be integers?

Factors are always whole numbers or integers and never decimals or fractions.

Is prime factorization NP-complete?

No, its not known to be NP-complete, and it would be very surprising if it were. This is because its decision version is known to be in NP∩co-NP. (Decision version: Does n have a prime factor

Why is prime factorization difficult?

In particular, it is hard to factor so-called RSA numbers which are of the form n = pq, where p and q are prime. Naively, the reason this is difficult is that you have to check every number between 0 and sqrt(n) until you find either p or q.

What does Shor algorithm do?

Shor’s algorithm is a quantum algorithm for factoring a number N in O((log N)3) time and O(log N) space, named after Peter Shor. The algorithm is significant because it implies that public key cryptography might be easily broken, given a sufficiently large quantum computer.

How does Shor algorithm work?

The basic gist of Shor’s algorithm is the process of period-finding which is done by the Quantum Fourier Transform (QFT). The QFT takes some function and figures out the period of the function. For example, if for all , then the function repeats itself every 10 values, and we can say that it has a period of 10.

Is factor a NP?

It is in NP, because a factor p such that p∣n serves as a witness of a yes instance. It is in co-NP because a prime factorization of n with no factors