The present disclosure relates to methods, devices, and systems for generating a signature of a message by a first device based on a secret key and a public key. The method includes generating a first parameter based on a first multiplication operation on the secret key and a first random number. The method further includes generating a first electronic signature based on the first parameter and the public key. The method further includes generating a second parameter based on the first random number, a second random number, and the message. The method further includes generating a second electronic signature based on the first parameter, the second parameter, the second random number, and the first electronic signature. The method further includes outputting, to a second device, the message, the first electronic signature, and the second electronic signature.