in computer sciencethe class of problems that computers can solve within polynomial time using step-wise process of logical steps is called -type problemswhere stands for polynomial these are relatively easy to solve then there is another class of problems that is considered very hard to solve the word "hard problemis used to refer to the way in which problems increase in difficulty when trying to find solution howeverthe good thing is that despite the fact that these problems have high growth rate of difficultyit is possible to determine whether proposed solution solves the problem in polynomial time these are the np-type problems np here stands for nondeterministic polynomial time now the million dollar question isdoes npthe proof for np is one of the millennium prize problems from the clay mathematics institute that attract $ , , prize for correct solution these problems number in number the travelling salesman problem is an example of an np-type problem the problem statement saysgiven that there are number of cities in some countryfind the shortest route between all the citiesthus making the trip cost-effective one when the number of cities is smallthis problem can be solved in reasonable amount of time howeverwhen the number of cities is above any two-digit numberthe time taken by the computer is remarkably long lot of computer systems and cybersecurity is based on the rsa encryption algorithm the strength of the algorithm and its security is due to the fact that it is based on the integer factoring problemwhich is an np-type problem finding the prime factors of prime number composed of many digits is very difficult when two large prime numbers are multiplieda large non-prime number is obtained with only two large prime factors factorization of this number is where many cryptographic algorithms borrow their strength