Code Breaking with a Quantum Computer

Abstract

Modern internet communications and electronic transactions rely heavily on the use of public key cryptosystems. Two famous examples are the RSA cryptosystem (RSA), and the elliptic curve cryptosystem (ECC). Such cryptosystems have the advantage that they do not require the sender and recipient of confidential messages to have met beforehand and exchanged secret key material. Instead, the person wishing to receive confidential messages creates a pair of matching public and private cryptographic keys, posts their public key for all to see, but keeps their private key secret. Anyone wishing to send the author of the public key a confidential message uses the posted public key to encrypt a message, and transmits the encrypted message via a potentially insecure classical communications channel. Upon receipt, the legitimate recipient uses his matching private key to unscramble the encrypted message.