Now that the transfer has been made, the two parties must verify that their keys match while maintaining the transfer's security. In Quantum Cryptography, this is a key step since random noise or eavesdroppers could induce problems into the transfer. The sender and the receiver can talk about groups of bits rather than individual ones and can compare the parity (the amount left over after dividing the total by two) within those groups to assure the greatest accuracy without disclosing the precise bits received. As long as the specifics are kept a secret, you can even do this in public.
Then, groups with parity disparities can be eliminated or divided into other groups, one or more of which can be eliminated or fixed (while still making sure the new groups are big enough to hide too much). In the end of Quantum Cryptography, this procedure ensures that the keys are arbitrarily similar if it is carried out frequently enough. Furthermore, the parity revealed is rendered meaningless to any listeners if, after comparing their groups of bits in this manner, the sender and the receiver drop an agreed-upon bit, such as the final one. Additionally, if desired, the received bit string, x, can be mapped into h(x), which can then be used as the key instead of x, using a publicly determined hash function, h. The eavesdropper's predicted knowledge of h(x) can be proved to be arbitrarily little by performing this.
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