The State of Elliptic Curve Cryptography

The State of Elliptic Curve Cryptography

19 (2000) | NEAL KOBILITZ, ALFRED MENEZES, SCOTT VANSTONE
The paper "The State of Elliptic Curve Cryptography" by Neal Koblitz, Alfred Menezes, and Scott Vanstone provides an overview of the development and current state of elliptic curve cryptosystems. The authors highlight the significance of the discrete logarithm problem in public-key cryptography, noting that while it was initially defined for multiplicative groups of integers modulo a prime, it can be extended to arbitrary groups, including elliptic curve groups. Elliptic curve cryptosystems offer several advantages over traditional systems, such as smaller key sizes, faster implementation, and reduced bandwidth requirements, making them particularly suitable for applications with limited computational power and space, like smart cards and wireless devices. The paper also discusses the elliptic curve analogues of the RSA cryptosystem, which, despite initial claims, do not offer significant advantages and are not considered in detail. The remainder of the paper covers a review of elliptic curves, the elliptic curve discrete logarithm problem, and implementation issues.The paper "The State of Elliptic Curve Cryptography" by Neal Koblitz, Alfred Menezes, and Scott Vanstone provides an overview of the development and current state of elliptic curve cryptosystems. The authors highlight the significance of the discrete logarithm problem in public-key cryptography, noting that while it was initially defined for multiplicative groups of integers modulo a prime, it can be extended to arbitrary groups, including elliptic curve groups. Elliptic curve cryptosystems offer several advantages over traditional systems, such as smaller key sizes, faster implementation, and reduced bandwidth requirements, making them particularly suitable for applications with limited computational power and space, like smart cards and wireless devices. The paper also discusses the elliptic curve analogues of the RSA cryptosystem, which, despite initial claims, do not offer significant advantages and are not considered in detail. The remainder of the paper covers a review of elliptic curves, the elliptic curve discrete logarithm problem, and implementation issues.
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