Editing Prepare and Measure Quantum Digital Signature (section)

==Outline==
Quantum Digital Signature (QDS) protocols can be separated into two stages: the distribution phase, where quantum signals (public keys) are sent to all recipients, and the messaging phase, where classical messages are signed, sent and verified. Here, we take the case of three parties, one sender (referred to as seller) and two receivers (buyer and verifier) sharing a one-bit message. 
Distribution phase can be divided into the following steps:
*'''	Key Distribution:''' Seller generates her (public key, private key) pair and shares the public key with both receivers in this step. For each possible message (0 or 1), she generates two identical sequences/copies (one for each receiver per possible message) of randomly chosen BB84 ∈ {0,1,+,−} states. The sequence of states is called quantum public key and its classical description, private key. She then sends copies of each quantum public key to the receivers while keeping both the private keys secret to herself. At the end of this step, the seller has two private keys, one for each possible message. Similarly, each receiver has two quantum public keys, one for each possible message.
*'''	State Elimination:''' Receivers store their classical records of the quantum public keys in this step. For each quantum public key received, a receiver randomly chooses pauli X or Z basis for each qubit and measures. Whatever outcome he gets, the receiver is certain that seller could not have generated a state orthogonal to his outcome. So, he records the state orthogonal to his outcome as the eliminated signature element. Such measurement is called ’Quantum State Elimination’. The sequence thus generated by measurement of all the qubits in a public key is called receiver’s eliminated signature for the respective quantum public key. Thus, each receiver finally has two eliminated signatures, one for each possible message.
*'''Symmetrisation:''' The two receivers exchange half of their randomly chosen eliminated signature elements. This prevents a dishonest seller to succeed in cheating by sending dissimilar public keys to the receivers. Thus ends the distribution phase.

Next the messaging phase is divided into the following steps:
*'''	Signing:''' Seller sends desired classical one-bit message and the corresponding private key to the desired receiver (called buyer). Buyer compares the private key with his eliminated signature for the corresponding message and counts the number of mismatches (eliminated signature element in seller’s private key).
*'''	Transfer:''' Buyer forwards the same message and private key to the other receiver (called verifier) who compares it with his eliminated signature for this message.