Prepare and Measure Quantum Digital Signature: Difference between revisions

This [[Prepare and Measure Quantum Digital Signature#Further Information|example protocol]] achieves the task of [[Quantum Digital Signature]] which allows for the exchange of single or multiple bit classical messages from sender to multiple recipients such that parties are required to prepare and measure quantum states instantly without having to store them. For simplicity, most protocols take into account the case of one sender and two recipients (Seller, buyer and verifier) exchanging single-bit classical messages.</br> It ensures that the sender (seller) cannot deny at a later stage having signed the message, a recipient (buyer) cannot fake or alter the QDS and another sender (verifier) can use the above two properties to verify if the sent message is signed by the genuine sender, thus, satisfying properties of  [[Quantum Digital Signature#Properties|transferability]],[[Quantum Digital Signature#Properties|non-repudiation]] and [[Quantum Digital Signature#Properties|unforgeability]]. It allows the user to sign electronic documents.</br>

*'''Honest majority assumption:''' assumes that more than number of participating parties are honest. In the present case at least two parties are honest.

Quantum Digital Signature (QDS) protocols can be separated into two stages: the distribution stage, where quantum signals (public keys) are sent to all recipients, and the messaging stage, 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.  

*''' 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, seller has two private keys, one for each possible message. Similarly, each receiver has two quantum public keys, one for each possible message.

*'''Symmetrisation:''' The two receivers exchange half of their randomly chosen eliminated signature elements. This prevents a dishonest seller succeed in cheating by sending dissimilar public keys to the receivers. Thus ends the distribution phase.

*''' 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).