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I have recently been reading about the general use of prime factors within cryptography. Everywhere i read, it states that there is no 'PUBLISHED' algorithm which operates in polynomial time (as opposed to exponential time), to find the prime factors of a key.
If an algorithm was discovered or published which did operate in polynomial time, then how would this impact in the real world computing environment as opposed to the world of theory and computer science. Considering the extent we depend on cryptography would the would suddenly come to halt.
With this in mind if P = NP is true, what might happen, how much do we depend on the fact that it is yet uproved.
I'm a beginner so please forgive any mistakes in my question, but i think you'll get my general gist.
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We can write 36 as a product of prime factors: 36 = 2² × 3². The expression 2² × 3² is said to be the prime factorization of 36.
What is the prime factorization of 90? The prime factorization of 90 is 2 × 3 × 3 × 5 or 2 × 32 × 5.
We know that 5 is a prime number, which means it has only two factors, i.e. 1 and 5. Thus, the only prime factor of 5 is the number itself.
With this in mind if N = NP is true, would they ever tell us.
Who are “they”? If it were true, we would know. The computer scientists? That’s us. The cryptographers and mathematicians? The professionals? The experts? People like us. Users of the Internet, even of Stack Overflow.
We wouldn’t need being told. We’d tell.
Science and research isn’t done behind closed doors. If someone finds out that P = NP, this couldn’t be kept secret, simply because of the way that research is published. In principle, everyone has access to such research.
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