This chapter excerpted from Hardware Implementation of Finite-Field Arithmetic, gives an example of finite-field application—namely, the implementation of the scalar product (point multiplication) ...

Editor's note: See the original article on PurpleAlientPlanet. Some of my research is focused on the implementation issues of elliptic curve cryptography on embedded systems. Since I often have to ...

Post-quantum cryptography is rapidly evolving to counter threats posed by quantum computing, and elliptic curves combined with isogeny methodologies offer a promising avenue. This approach leverages ...

We all know the usual jokes about the ‘S’ in ‘IoT’ standing for ‘Security’. It’s hardly a secret that security in embedded, networked devices (‘IoT devices’) is all too often a last-minute task that ...

Encryption is a key technology for federal agencies. Although encryption is the primary goal, many encryption systems depend on a combination of tools to accomplish other tasks. Public-key ...

“Elliptic curve cryptography (ECC), as one of the public key cryptography systems, has been widely applied to many security applications. It is challenging to implement a scalar multiplication (SM) ...

The mathematicians who toiled on the famous enigma also devised powerful forms of end-to-end encryption. By William J. Broad Defenses against digital snoopers keep getting stronger. Encryption is what ...

Manjul Bhargava was warned long ago never to think about math while driving. "I find doing mathematical research requires very deep concentration," said Bhargava, the Brandon Fradd, Class of 1983, ...

The elliptic curve discrete logarithm problem (ECDLP) lies at the heart of modern public-key cryptography. It concerns the challenge of determining an unknown scalar multiplier given two points on an ...

According to one of the world’s leading cryptographers, Bitcoin’s elliptic curve could have a secret backdoor, invalidating all underlying security. A Bitcoin public key is created by applying ...