elliptic curve
Noun
Meaning
elliptic curve (plural elliptic curves)
(algebraic geometry) The algebraic set of an equation which equates the square of one variable to a reduced cubic polynomial in another variable, over some field, and such that the discriminant of the reduced cubic is non-zero.
Synonyms
Examples
NIST’s post-quantum standard is necessary because it has been shown that quantum computers can easily factorise large numbers and it is now a matter of time before today’s public-key cryptography standards (RSA and Elliptic Curve) are broken.
It uses elliptic curve isogenies to create a drop-in replacement for the quantum attackable Diffie–Hellman and Elliptic curve Diffie–Hellman key exchanges.
Elliptic curve cryptography that use short keys, for example 192 bit ECDSA, will be at risk earlier than older schemes using longer keys (3072 bit RSA).
Microsoft’s advisory, the spoofing vulnerability exists in the way Windows CryptoAPI (Microsoft’s API that enables developers to secure Windows-based applications using cryptography) validates Elliptic Curve Cryptography (ECC) certificates.
Elliptic curve cryptography may allow smaller-size keys for equivalent security, but these algorithms have only been known for a relatively short time and current estimates of the difficulty of searching for their keys may not survive.
Section 7.4: Elliptic curve method, pp. 301–313.