Gottesman and Chuang Quantum Digital Signature

Functionality Description

Digital Signatures (QDS) allow the exchange of classical 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 (i) 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, (ii) non-repudiation i.e at any stage after sending the message to one recipient, sender cannot deny having sent the message and corresponding DS, and (iii) unforgeability i.e. a dishonest recipient cannot alter or fake the sender's DS and forward it to other recipients successfully.
Such protocols require parties to store quantum states for comparison at a later stage. For simplicity, most protocols take into account the case of one sender and two recipients (Seller, buyer and verifier) exchanging single-bit classical messages.

Tags: Multi Party (three), Quantum Enhanced Classical Functionality, Specific Task, Quantum Digital Signature, Prepare and Measure Quantum Digital Signature, Measurement Device Independent Quantum Digital Signature (MDI-QDS)

Requirements

• Network Stage:Quantum Memory
• Relevant Network Parameters:
• Benchmark values:

Example:

Outline

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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. Distribution phase can be divided into the following steps:

• Key Distribution:

Similarly, Messaging Phase is divided into the following steps:

• Signing:
• Transfer:

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Pseudo Code

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• Notations Used:

Further Information

Theoretical Papers

1. GC-QDS (2001) uses quantum one way function f(); Private keys: classical input x, Public keys: quantum output f(x).
   1. Requires quantum memory, quantum one way function, authenticated quantum and classical channels, SWAP Test (universal quantum computer).
   2. Security: Information-theoretic
2. ACJ (2006) discusses coherent states comparison with a QDS scheme outlined in the last section.
   1. Protocol uses the same protocol as (2) but replaces qubits with coherent states, thus replacing SWAP-Test with Coherent State Comparison. Additionally, it also requires quantum memory, authenticated quantum and classical channels, multiports.
   2. Security: Information-theoretic
3. SWZY (2017) Discusses an attack and suggests corrections on existing QDS scheme using single qubit rotations. Protocol uses rotation, qubits, one-way hash function; Private keys: angle of rotation, Public keys: string of rotated quantum states.
   1. Requires random number generator, one-way hash function, quantum memory, key distribution.
   2. Security: Computational

Experimental Papers

1. CCDAJB (2012) uses phase encoded coherent states, coherent state comparison
   1. Loss from multiport=7.5 dB, Length of the key= $10^{6}$

*contributed by Shraddha Singh