Method for genertaing a digital signature

An electronic device comprising:

• a central processing unit;
• and
• a main system memory operatively connected to a central processing unit having instructions stored thereon that, when executed on the central processing unit, cause the central processing unit to:
• calculate a first magnitude representative of the inverse of a random number raised at least to the power two;
• obtain a first element of the digital signature by executing a scalar multiplication between the random number and the established point on the elliptic curve and then taking the x-coordinate of the result point;
• obtain a second magnitude by executing a modular multiplication, with modulus corresponding to the established elliptic curve's order between the first magnitude and one of the secret encryption key or the first element of the digital signature;
• obtain a third magnitude by executing a modular multiplication, with modulus corresponding to the established elliptic curve's order between the random number and one of the secret encryption key or the first element of the digital signature;
• obtain a first addend of a second element of the digital signature by executing a modular multiplication, with modulus corresponding to the established elliptic curve's order between the second magnitude and the third magnitude;
• and
• generate a second element of the digital signature based at least in part on the obtained first addend.

A non-transitory computer-readable medium having computer-executable instructions stored thereon that, when executed on a computer, cause the computer to:

• calculate a first magnitude representative of the inverse of a random number raised at least to the power two;
• obtain a first element of the digital signature by executing a scalar multiplication between an established point of the established elliptic curve and the random number;
• obtain a second magnitude by executing a modular multiplication, with modulus corresponding to the established elliptic curve's order between the first magnitude and one of the secret encryption key or the first element of the digital signature;
• obtain a third magnitude by executing a modular multiplication, with modulus corresponding to the established elliptic curve's order between the random number and one of the secret encryption key or the first element of the digital signature;
• obtain a first addend of a second element of the digital signature by executing a modular multiplication, with modulus corresponding to the established elliptic curve's order between the second magnitude and the third magnitude;
• and
• generate a second element of the digital signature based at least in part on the obtained first addend.