Two teams of physicists have independently confirmed that 15 equals 3 times 5—an arduous task considering that they've done it by manipulating the quantum states of photons. The results are a step toward optical quantum computers, which could do some calculations exponentially faster than ordinary computers can and crack the encryption codes that protect data traveling over the Internet.
Multiplying two whole numbers is easy, but the inverse operation generally isn't: Identifying when a number is the product of other whole numbers becomes exponentially more complex as the numbers get bigger, quickly overwhelming even the fastest supercomputers.
This is good for privacy. When Web-based programs request sensitive data over the Internet, they ask the sender's Web browser to encrypt the data using a number, called the public key, that is the product of two prime numbers. Decrypting the data requires identifying those two prime numbers, which only the legitimate recipi