| CPC H04L 9/3247 (2013.01) [H04L 9/0825 (2013.01); H04L 9/083 (2013.01); H04L 9/0869 (2013.01); H04L 9/3006 (2013.01)] | 18 Claims |

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1. A method of generating a signature of a message by a first device based on a secret key and a public key, the method comprising:
generating a first parameter based on a first multiplication operation on the secret key and a first random number;
generating, using a signature generation circuit, a first electronic signature based on the first parameter and the public key;
generating a second parameter by performing a second multiplication operation of a hash function of the message, the first random number, and an inverse of a second random number, and performing a first modular operation based on a result of the second multiplication operation and a prime number;
generating, using the signature generation circuit, a second electronic signature by performing a third multiplication operation of the first parameter and the second random number, performing a fourth multiplication operation of an inverse of a result of the third multiplication operation and the first electronic signature, performing a second modular operation based on a result of the fourth multiplication operation and the prime number, and performing an addition operation on a result of the second modular operation and the second parameter;
combining, using a combining circuit, the message, the first electronic signature, and the second electronic signature to generate a combination message; and
transmitting, to a second device over a channel, the combination message, causing the second device to obtain validity information, using a verification circuit, certifying the combination message that has been transmitted by the first device, the validity information being based on the message, the first electronic signature, and the second electronic signature.
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