In the not-too-distant future—as little as a decade, perhaps, nobody knows exactly how long—the cryptography protecting your bank transactions, chat messages, and medical records from prying eyes is going to break spectacularly with the advent of quantum computing. On Tuesday, a US government agency named four replacement encryption schemes to head off this cryptopocalypse.
Some of the most widely used public-key encryption systems—including those using the RSA, Diffie-Hellman, and elliptic curve Diffie-Hellman algorithms—rely on mathematics to protect sensitive data. These mathematical problems include (1) factoring a key's large composite number (usually denoted as N) to derive its two factors (usually denoted as P and Q) and (2) computing the discrete logarithm that keys are based on.
The security of these cryptosystems depends entirely on classical computers' difficulty in solving these problems. While it's easy to generate keys that can encrypt and decrypt data at will, it's impossible from a practical standpoint for an adversary to calculate the numbers that make them work.