My 82-year-old mother never was very good at arithmetic. She now has lost the ability to balance her checkbook. Yet this morning, at the touch of a button on her browser, she performed a fairly sophisticated arithmetic operation on her way to establishing a secure session with the e-commerce site where she orders her medications. This operation is called "modular exponentiation." If Mom knew its nine-syllable name she would have been afraid to push the button. Fortunately, and crucially, the operation is hidden from her, as it is from most of us. It is part of a cryptographic system, a system designed to provide confidential communication.

To Mom's eternal puzzlement, I am a cryptographer, an expert in making and breaking secrets. Cryptography is at least as old as writing. Indeed, before the rise of literacy, writing itself was a form of cryptography. Written messages among literate people could safely be transmitted via illiterate couriers. The spread of literacy led to the invention of ways to obscure the meaning of a message-for example, reordering letters, or substituting some letters for others. Modern cryptographic algorithms still rely on reordering and substitution. But of course, we now use computers to manipulate the symbols.