Elliptic Curve Cryptosystem

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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. The use of elliptic curves in cryptography was suggested independently by Neal Koblitz[1] and Victor S. Miller[2] in 1985.… …   Wikipedia

• Elliptic Curve Cryptography — Elliptische Kurve über Unter Elliptic Curve Cryptography (ECC) oder deutsch Elliptische Kurven Kryptographie versteht man asymmetrische Kryptosysteme, die Operationen auf elliptischen Kurven über endlichen Körpern v …   Deutsch Wikipedia

• Counting points on elliptic curves — An important aspect in the study of elliptic curves is devising effective ways of counting points on the curve. There have been several approaches to do so, and the algorithms devised have proved to be useful tools in the study of various fields… …   Wikipedia

• McEliece cryptosystem — In cryptography, the McEliece cryptosystem is an asymmetric encryption algorithm developed in 1978 by Robert McEliece.[1] It was the first such scheme to use randomization in the encryption process. The algorithm has never gained much acceptance… …   Wikipedia

• Hyperelliptic curve — In algebraic geometry, a hyperelliptic curve (over the complex numbers) is an algebraic curve given by an equation of the form:y^2 = f(x)where f(x) is a polynomial of degree n > 4 with n distinct roots. A hyperelliptic function is a function from …   Wikipedia

• Cramer–Shoup cryptosystem — The Cramer–Shoup system is an asymmetric key encryption algorithm, and was the first efficient scheme proven to be secure against adaptive chosen ciphertext attack using standard cryptographic assumptions. Its security is based on the… …   Wikipedia

• Naccache–Stern cryptosystem — Note: this is not to be confused with the Naccache–Stern knapsack cryptosystem. The Naccache–Stern cryptosystem is a homomorphic public key cryptosystem whose security rests on the higher residuosity problem. The Naccache–Stern cryptosystem was… …   Wikipedia

• Naccache–Stern knapsack cryptosystem — Note: this is not to be confused with the Naccache–Stern cryptosystem based on the higher residuosity problem. The Naccache–Stern Knapsack Cryptosystem is an atypical public key cryptosystem developed by David Naccache and Jacques Stern in 1997.… …   Wikipedia

• Niederreiter cryptosystem — In cryptography, the Niederreiter cryptosystem is a variation of the McEliece Cryptosystem developed in 1986 by Harald Niederreiter [1]. It applies the same idea to the parity check matrix H of a linear code. Niederreiter is equivalent to… …   Wikipedia

• Damgård–Jurik cryptosystem — The Damgård–Jurik cryptosystem[1] is a generalization of the Paillier cryptosystem. It uses computations modulo ns + 1 where n is an RSA modulus and s a (positive) natural number. Paillier s scheme is the special case with s = 1. The order φ(ns + …   Wikipedia

• Merkle–Hellman knapsack cryptosystem — The Merkle–Hellman knapsack cryptosystem was one of the earliest public key cryptosystems invented by Ralph Merkle and Martin Hellman in 1978.[1] Although its ideas are elegant, and far simpler than RSA, it has been broken.[2] Contents 1… …   Wikipedia