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Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in Galois fields, such as the RSA cryptosystem and ElGamal cryptosystem.
Hewlett-Packard holds U.S. patent 6,252,960 on compression and decompression of data points on elliptic curves. It expired in 2018. According to the NSA, Certicom holds over 130 patents relating to elliptic curves and public key cryptography in general. [5] It is difficult to create a complete list of patents that are related to ECC.
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 ...
The difficulty of this problem is the basis for the security of several cryptographic systems, including Diffie–Hellman key agreement, ElGamal encryption, the ElGamal signature scheme, the Digital Signature Algorithm, and the elliptic curve cryptography analogues of these.
The security of the scheme is based on the computational Diffie–Hellman problem. Two variants of IES are specified: Discrete Logarithm Integrated Encryption Scheme (DLIES) and Elliptic Curve Integrated Encryption Scheme (ECIES), which is also known as the Elliptic Curve Augmented Encryption Scheme or simply the Elliptic Curve Encryption Scheme.
Formally, is a generator of some group (typically the multiplicative group of a finite field or an elliptic curve group) and and are randomly chosen integers. For example, in the Diffie–Hellman key exchange, an eavesdropper observes g x {\displaystyle g^{x}} and g y {\displaystyle g^{y}} exchanged as part of the protocol, and the two parties ...
Elliptic curve cryptography is a popular form of public key encryption that is based on the mathematical theory of elliptic curves. Points on an elliptic curve can be added and form a group under this addition operation. This article describes the computational costs for this group addition and certain related operations that are used in ...
In cryptography, Curve25519 is an elliptic curve used in elliptic-curve cryptography (ECC) offering 128 bits of security (256-bit key size) and designed for use with the Elliptic-curve Diffie–Hellman (ECDH) key agreement scheme. It is one of the fastest curves in ECC, and is not covered by any known patents. [1]