Editing Uncloneable Encryption (section)

==Outline==

The protocol requires a pre-shared set of four keys that are partially consumed in the protocol and that can be regenerated by using the protocol itself.

===Encoding phase:===

The message is divided into parts (registers). A polynomial of degree equal to the number of parts is defined with the value of the registers as its coefficients. The constant term is chosen such that the first key value is a root of the polynomial. The string formed by coefficients of the polynomial is then XORed with the second key value. This classical pre-processing step is reminiscent to Shamir Secret Sharing scheme.

Both codes are then used in conjunction with the obtained string to pick a string to encode the pre-processed string such that the first one offers error protection against noise in the channel and the second one for privacy amplification.

The obtained classical string is then encoded in the computational or Hadamard basis according to the corresponding bit in the fourth key value and sent to the receiver.

===Decoding phase:===

Upon receiving the qubits, they are measured in the computational or Hadamard basis according to the corresponding bit in the fourth key value.

Calculate the parity checks of the first classical code. If they are not equal to the third shared key value, there are errors in the state, which can be corrected using the standard decoding map. Evaluate the parity checks of <math>C_2/C_1^{\perp}</math>, producing another string.
    
The string obtained is XORed with the second key value and used as coefficients of a polynomial. The polynomial is then evaluated at the first key value and if it gives zero, the message is accepted. It is rejected otherwise.