Quantum signature method and quantum secret sharing method using quantum trapdoor one-way function

A quantum signature method comprising:

• (a) generating, by a transmitter, a quantum message |M;
• (b) generating, by the transmitter, a private key and a public key by using two rotation operators R{circumflex over (n)}(θ) and R{circumflex over (m)}(φ) satisfying a cyclic evolution;
• (c) generating, by the transmitter, a quantum signature |S by applying the rotation operators R{circumflex over (n)}(θ) and R{circumflex over (m)}(φ);
• and
• (d) transmitting, by the transmitter, a quantum signature pair |M⊗|S including the quantum message |M and the quantum signature |S to a receiver.

A method of sharing a quantum secret, the method comprising:

• (a) generating, by a secret generator, a quantum secret |S;
• (b) generating, by the secret generator, an encryption key and a decryption key by using two rotation operators R{circumflex over (n)}(θ) and R{circumflex over (m)}(φ) satisfying a cyclic evolution;
• (c) generating, by the secret generator, an encrypted quantum secret |S′ from the quantum secret by using the encryption key;
• (d) dividing, by the secret generator, the decryption key into N pieces and transmitting the N pieces of decryption key to a plurality of secret receivers;
• and
• (e) transmitting, by the secret generator, the encrypted quantum secret |S″ to a secret verifier.