Final answer:
Cryptographic algorithms rely on the characteristic of one-way functions, which are easy to perform but difficult to reverse without specific information, for security.
Step-by-step explanation:
The characteristic of the problem of factoring the product of large prime numbers that cryptographic algorithms rely on is that it is a one-way function. A one-way function is an operation that is easy to perform in one direction, in this case, multiplying two large primes to obtain a product, but very difficult to reverse without special information, namely the original prime factors. This difficulty ensures the security of cryptographic algorithms since even if an attacker knows the product (the public key), without the primes it's practically impossible to decrypt the information.