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Prepare and Measure Quantum Digital Signature (edit)
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Digital Signatures (DS) allow for the exchange of messages from sender to multiple recipients, with a guarantee that the signature has come from a genuine sender. Additionally, it comes with the properties of transferability, i.e. messages with DS can be forwarded from one recipient to another such that DS is verifiable to have come from the original sender, and non-repudiation, i.e at any stage after sending the message to one recipient, sender cannot deny having sent the message and corresponding DS.<br/> | Digital Signatures (DS) allow for the exchange of messages from sender to multiple recipients, with a guarantee that the signature has come from a genuine sender. Additionally, it comes with the properties of transferability, i.e. messages with DS can be forwarded from one recipient to another such that DS is verifiable to have come from the original sender, and non-repudiation, i.e at any stage after sending the message to one recipient, sender cannot deny having sent the message and corresponding DS.<br/> | ||
== | ==Use Case== | ||
Online Transactions, Signing Marksheets | Online Transactions, Signing Marksheets | ||
'''Tags:''' [[Multi Party Protocols|Multi Party (three)]], [[Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[Specific Task|Specific Task]], [[Measurement Device Independent Quantum Digital Signature|Measurement Device Independent Quantum Digital Signature (MDI-QDS)]] | '''Tags:''' [[Multi Party Protocols|Multi Party (three)]], [[Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[Specific Task|Specific Task]], [[Measurement Device Independent Quantum Digital Signature|Measurement Device Independent Quantum Digital Signature (MDI-QDS)]] | ||
== Example:https://arxiv.org/abs/1403.5551 == | |||
==Outline== | ===Outline=== | ||
Quantum Digital Signature (QDS) protocols can be separated into two stages: the distribution stage, where quantum public keys are sent to all recipients, and the messaging stage, where classical messages are 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. Following protocol requires Client to prepare and send quantum public keys to the buyer and verifier, hence the name, ''Prepare and Send QDS''. | Quantum Digital Signature (QDS) protocols can be separated into two stages: the distribution stage, where quantum public keys are sent to all recipients, and the messaging stage, where classical messages are 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. Following protocol requires Client to prepare and send quantum public keys to the buyer and verifier, hence the name, ''Prepare and Send QDS''. | ||
Distribution phase can be divided into the following steps: | 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, seller has two private keys, one for each possible message. Similarly, each receiver has two quantum public keys, one for each possible 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. | ||
*''' 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 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. | *''' 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 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 succeed in cheating by sending dissimilar public keys to the receivers. Thus ends the distribution phase. | *'''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. | ||
Similarly, Messaging Phase is divided into the following steps: | Similarly, Messaging Phase is divided into the following steps: | ||
*''' Signing:''' Seller sends desired 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). | *''' Signing:''' Seller sends desired 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). | ||
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Figure | Figure | ||
== | === Requirements === | ||
*L : length of quantum public keys (a security parameter). | *L : length of quantum public keys (a security parameter). | ||
*<math>s_a:</math> authentication threshold per qubit. | *<math>s_a:</math> authentication threshold per qubit. | ||
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===Properties=== | ===Properties=== | ||
---- | ---- | ||
*This protocol requires no quantum memory. | *This protocol requires no quantum memory. | ||
*The protocol assumes maximum number of participating parties are honest. In the present case at least two parties are honest. | *The protocol assumes maximum number of participating parties are honest. In the present case at least two parties are honest. | ||