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, ...

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 ...

A public key cryptography method that provides fast decryption and digital signature processing. Elliptic curve cryptography (ECC) uses points on an elliptic curve to derive a 163-bit public key that ...

Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there ...

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 ...

Si E₁ et E₂ sont deux courbes elliptiques sur un corps k, nous avons une application naturelle CH¹(E₁)₀ ⊗ CH¹(E₂)₀ → CH²(E₁ × E₂). Quand k est un corps de nombres, une conjecture due à Bloch et ...

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 ...

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 ...

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 ...