Advanced Placement (AP) Computer Science

What is a key property of prime numbers that makes them useful for internet security?

1. They can be easily factored

2. They are predictable and repeat

3. They are challenging to factorize

4. They have a unique pattern

The correct answer is: They are challenging to factorize

Prime numbers play a crucial role in internet security, particularly in encryption algorithms such as RSA. The key property that makes them useful is that they are challenging to factorize. When a large number is the product of two prime numbers, finding those two primes is computationally difficult. This difficulty is what provides the security backbone of many encryption methods used to protect sensitive information online. While other options may suggest certain mathematical attributes, they do not support the premise of enhanced security. For instance, the concept of predictability implies that if prime numbers were easily predictable or formed a repeatable pattern, this would undermine their efficacy in security applications, as an attacker could more readily attempt to exploit these patterns to break encryptions. A unique pattern would similarly provide a predictable structure that could be exploited. The statement about easy factorization starkly opposes the essential characteristic that underpins prime usage in cryptography.