After a multi-year competition, the U.S. National Institute of Standards and Technology (NIST) selected a suite of algorithms for standardization. For key exchange, the primary choice is the ...

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, ...

When it comes to public key cryptography, most systems today are still stuck in the 1970s. On December 14, 1977, two events occurred that would change the world: Paramount Pictures released Saturday ...

Elliptic curve cryptography (ECC) has emerged as a cornerstone of modern public‐key systems, offering high levels of security with relatively small key sizes. Central to many advanced cryptographic ...

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 ...

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 ...

The NSA is moving away from Elliptic Curve Cryptography, and cryptographers aren’t buying their reasoning that advances in post quantum computing put ECC in jeopardy. The National Security Agency has ...

At a prime of ordinary reduction, the Iwasawa "main conjecture" for elliptic curves relates a Selmer group to a p-adic L-function. In the supersingular case, the statement of the main conjecture is ...

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others. You’re sitting at the end of a long conference table, ...

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves. Elliptic curves seem to admit infinite variety, but they really only come in two flavors. That ...