Difference between revisions of "Prepare-and-Measure Certified Deletion"

From Quantum Protocol Zoo
Jump to: navigation, search
m
 
Line 26: Line 26:
 
* <math>\lambda</math>: Security parameter
 
* <math>\lambda</math>: Security parameter
 
* <math>n</math>: Length, in bits, of the message
 
* <math>n</math>: Length, in bits, of the message
 +
* <math>\omega : \{0,1\} \rightarrow \mathbb{N}</math> : Hamming weight function
 
* <math>m = \kappa(\lambda)</math>: Total number of qubits sent from encrypting party to decrypting party
 
* <math>m = \kappa(\lambda)</math>: Total number of qubits sent from encrypting party to decrypting party
 
* <math>k</math>: Length, in bits, of the string used for verification of deletion
 
* <math>k</math>: Length, in bits, of the string used for verification of deletion

Latest revision as of 01:25, 9 February 2022


This example protocol implements the functionality of Quantum Encryption with Certified Deletion using single-qubit state preparation and measurement. This scheme is limited to the single-use, private-key setting.

Requirements[edit]

Outline[edit]

The scheme consists of 5 circuits-

  • Key: This circuit generates the key used in later stages
  • Enc: This circuit encrypts the message using the key
  • Dec: This circuit decrypts the ciphertext using the key and generates an error flag bit
  • Del: This circuit deletes the ciphertext state and generates a deletion certificate
  • Ver: This circuit verifies the validity of the deletion certificate using the key

Notation[edit]

  • For any string and set denotes the string restricted to the bits indexed by
  • For
  • denotes the state space of a single qubit,
  • denotes the set of density operators on a Hilbert space
  • : Security parameter
  • : Length, in bits, of the message
  •  : Hamming weight function
  • : Total number of qubits sent from encrypting party to decrypting party
  • : Length, in bits, of the string used for verification of deletion
  • : Length, in bits, of the string used for extracting randomness
  • : Length, in bits, of error correction hash
  • : Length, in bits, of error syndrome
  • : Basis in which the encrypting party prepare her quantum state
  • : Threshold error rate for the verification test
  • : Set of possible bases from which \theta is chosen
  • : Universal family of hash functions used in the privacy amplification scheme
  • : Universal family of hash functions used in the error correction scheme
  • : Hash function used in the privacy amplification scheme
  • : Hash function used in the error correction scheme
  • : Function that computes the error syndrome
  • : Function that computes the corrected string

Protocol Description[edit]

Circuit 1: Key[edit]

The key generation circuit

Input : None

Output: A key state

  1. Sample
  2. Sample where
  3. Sample
  4. Sample
  5. Sample
  6. Sample
  7. Sample
  8. Output

Circuit 2: Enc[edit]

The encryption circuit

Input : A plaintext state and a key state

Output: A ciphertext state

  1. Sample where
  2. Compute where
  3. Compute
  4. Compute
  5. Output

Circuit 3: Dec[edit]

The decryption circuit

Input : A key state and a ciphertext

Output: A plaintext state and an error flag

  1. Compute
  2. Measure in the computational basis. Call the result
  3. Compute where
  4. Compute
  5. If , then set . Else, set
  6. Compute
  7. Output

Circuit 4: Del[edit]

The deletion circuit

Input : A ciphertext

Output: A certificate string

  1. Measure in the Hadamard basis. Call the output y.
  2. Output

Circuit 5: Ver[edit]

The verification circuit

Input : A key state and a certificate string

Output: A bit

  1. Compute where
  2. Compute
  3. If , output . Else, output .

Properties[edit]

This scheme has the following properties:

  • Correctness: The scheme includes syndrome and correction functions and is thus robust against a certain amount of noise, i.e. below a certain noise threshold, the decryption circuit outputs the original message with high probability.
  • Ciphertext Indistinguishability: This notion implies that an adversary, given a ciphertext, cannot discern whether the original plaintext was a known message or a dummy plaintext
  • Certified Deletion Security: After producing a valid deletion certificate, the adversary cannot obtain the original message, even if the key is leaked (after deletion).

References[edit]

*contributed by Chirag Wadhwa