To check for the presence of an eavesdropper, Alice and Bob now compare a predetermined subset of their remaining bit strings. If a third party (usually referred to as Eve, for "eavesdropper") has gained any information about the photons' polarization, this introduces errors in Bob's measurements. Other environmental conditions can cause errors in a similar fashion. If more than formula_1 bits differ they abort the key and try again, possibly with a different quantum channel, as the security of the key cannot be guaranteed. formula_1 is chosen so that if the number of bits known to Eve is less than this, privacy amplification can be used to reduce Eve's knowledge of the key to an arbitrarily small amount at the cost of reducing the length of the key.