Curve448 | EPFL Graph Search

In cryptography, Curve448 or Curve448-Goldilocks is an elliptic curve potentially offering 224 bits of security and designed for use with the elliptic-curve Diffie–Hellman (ECDH) key agreement scheme. Developed by Mike Hamburg of Rambus Cryptography Research, Curve448 allows fast performance compared with other proposed curves with comparable security. The reference implementation is available under an MIT license. The curve was favored by the Internet Research Task Force Crypto Forum Research Group (IRTF CFRG) for inclusion in Transport Layer Security (TLS) standards along with Curve25519. In 2017, NIST announced that Curve25519 and Curve448 would be added to "Special Publication 800-186", which specifies approved elliptic curves for use by the US Federal Government, and in 2023 it was approved for use in FIPS 186-5. Both are described in . The name X448 is used for the DH function. Hamburg chose the Solinas trinomial prime base p = 2448 − 2224 − 1, calling it a "Goldilocks" prime "because its form defines the golden ratio φ ≡ 2224". The main advantage of a golden-ratio prime is fast Karatsuba multiplication. The curve Hamburg used is an untwisted Edwards curve Ed: y2 + x2 = 1 − 39081x2y2. The constant d = −39081 was chosen as the smallest absolute value that had the required mathematical properties, thus a nothing-up-my-sleeve number. Curve448 is constructed such that it avoids many potential implementation pitfalls.

When Constant-time Source Yields Variable-time Binary: Exploiting Curve25519-donna Built with MSVC 2015

Serge Vaudenay

The elliptic curve Curve25519 has been presented as pro- tected against state-of-the-art timing attacks [2]. This paper shows that a timing attack is still achievable against a particular X25519 implemen- tation which follows the RFC 7748 requirements [11] ...

Springer Int Publishing Ag2016

High-Performance Modular Multiplication on the Cell Processor

Joppe Willem Bos

This paper presents software implementation speed records for modular multiplication arithmetic on the synergistic processing elements of the Cell broadband engine (Cell) architecture. The focus is on moduli which are of special interest in elliptic curve ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010

High-Performance Modular Multiplication on the Cell Processor

Joppe Willem Bos

Springer Berlin Heidelberg2010