the problem of determining which numbers from a given collection of numbers have been added together to yield a specific sum: used in cryptography to encipher (and sometimes decipher) messages.
Origin of knapsack problem
so called because the problem is similar to determining what packages are in a closed knapsack when the weights of the individual packages and the filled knapsack are known
application, mathematics Given a set of items, each with a cost and a value, determine the number of each item to include in a collection so that the total cost is less than some given cost and the total value is as large as possible. The 0/1 knapsack problem restricts the number of each items to zero or one. Such constraint satisfaction problems are often solved using dynamic programming. The general knapsack problem is NP-hard, and this has led to attempts to use it as the basis for public-key encryption systems. Several such attempts failed because the knapsack problems they produced were in fact solvable by polynomial-time algorithms. [Are there any trusted knapsack-based public-key cryptosystems?]. (1995-04-10)