Writing a strong Crypto Algo

Do you know watz the basics of Strong crypto algos like RSA, Elliptic curve cryptography etc.. Itz the Mathematical problem associated with it. What happens is, you take an unsolvable Mathematical problem and associate with an encryption scheme. For eg, RSA Algorithm is associated with Prime Integer Factorization problem. It is not feasible with the current computing power to break the factors of the private Key

In mathematics, the integer prime-factorization (also known as prime decomposition) problem is this: given a positive integer, write it as a product of prime numbers. For example, given the number 45, the prime factorization would be 32·5. The factorization is always unique, according to the fundamental theorem of arithmetic. This problem is of significance in mathematics, cryptography, complexity theory, and quantum computing.

Anyone knows how exactly the Prime Integer Factorization problem gets interfaced with RSA ? I'll write about this later...

Anywayz if you get some NP-hard or NP-complete problem, maybe you shud try to generate a strong crypto algo out of it.