@lotuseclat79 Do you know why public key encryption uses primes ? I understand the principle of the trap door function but why does it have to be a prime?
Hi RockLobster, Prime numbers are used because the factorization of very large prime numbers often takes more time than is practical for normal computers except for nation states with the computer resources to make such computations. -- Tom
Yes but if I took any two 1024 bit numbers and multiplied them together and gave you the product it would be impossible for you to tell me the two factors I used regardless of whether they were prime or not. I am heavily skeptical I do not trust anything until I have been over it myself. I want to satisfy myself that rsa does not use primes because they had a secret way of factoring them that no one but they and the government knows. I have searched for the answer but have not found anyone who can say why they must be prime.
Your assumption that "any two 1024 bit numbers" is the foundation of your argument - and it will get you into trouble every time you cannot verify that the two numbers you have chosen are up to the quality that prime numbers (read that as at least an order of magnitude harder to factor than non-prime numbers) represent in the field of cryptography. Ask yourself the question "Can I prove my assumptions"? Download the following PDF document... The science of encryption: prime numbers and mod n arithmetic https://math.berkeley.edu/~kpmann/encryption.pdf -- Tom
What do prime numbers have to do with encryptions? And what does the difficulty in factoring prime numbers have to do with breaking algorithms? -- Tom
@lotuseclt79 I don't know what you mean when you suggested an ordinary 1024 bit number may not be up to the quality of a 1024 bit prime. The main differences between primes and an ordinary numbers is the prime has no factors and the product of two primes (the semiprime from which the public key is derived) has only those two primes as its factors. Wheras the product of two ordinary 1024 bit numbers would have many factors only 2 of which would be the co rrect ones.
No I cant prove any assumptions and I see where you say it is an order of magnitude more difficult to factor primes than ordinary numbers. If that is true it is the answer I was looking for to satisfy my curiosity on this.
I still have not found mathematical evdence that factoring primes is any different than factoring ordinary numbers except that when you know the factors are prime it means less possibilities to check and for example if you work in base 6, ALL primes end in 1 or 5. It's like this, when you have state approved encryption, one of two things happened. Either that government approved uncrackable encryption while knowing all their potential enemies could also use it, OR they were smarter than that. You dont see US polititians hopping up and down demanding backdoors like the British ones. Why not?
