Abstract: A method includes receiving a first input value and a second input value, and obtaining a set of pre-computed values, wherein each pre-computed value is computed as the first input value multiplied by a given multiple in a set of multiples comprising powers of 2. A cryptographic process is performed to generate a cryptographic value based on the first and second input values, and one or more of the pre-computed values, wherein the cryptographic value that is generated is usable to generate a secure message or digital signature. The cryptographic process includes performing an iterative scalar multiplication process in which each step of the iterative scalar multiplication process is performed using a single point add operation to multiply a bit of the second input value with one of the pre-computed values in the set of pre-computed values.

Abstract: A blinding function is generated. The blinding function is applied to a random value to generate a blinded random value. The blinded random value is utilized for one or more scalar multiplications in an elliptic curve cryptographic operation.

Abstract: Embodiments relate to a method for generating a set of authentication certificates by a set of certificate authority devices. The method includes receiving, by the set of certificate authority devices, a set of certificate requests from a user device. The method includes generating, by the set of certificate authority devices, a set of crosschecked certificates, each crosschecked certificate of the set of crosschecked certificates being configured to cryptographically verify the remaining crosschecked certificate of the set of crosschecked certificates. The method includes transmitting, by the set of certificate authority devices, the set of crosschecked certificates to the user device, the set of crosschecked certificates configured to be utilized by the user device in establishing a secured communication channel over a network between the user device and a client device.