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Publication# Efficient identity based parameter selection for elliptic curve cryptosystems

Abstract

A method is proposed that allows each individual party to an elliptic curve cryptosystem to quickly determine its own unique pair of finite field and Weierstrass equation, in such a way that the resulting pair provides adequate security. Although the choice of Weierstrass equations allowed by this proposal is limited, the number of possible finite fields is unlimited. The proposed method allows each participant to select its elliptic curve cryptosystem parameters in such a way that the security is not affected by attacks on any other participant unless unanticipated progress is made affecting the security for a particular Weierstrass equation irrespective of the underlying finite field. Thus the proposal provides more security than elliptic curve cryptosystems where all participants share the same Weierstrass equation and finite field. It also offers much faster and less complicated parameter initialization than elliptic curve cryptosystems where each participant randomly selects its own unique Weierstrass equation and thus has to solve the cumbersome point counting problem

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Related concepts (30)

Elliptic-curve cryptography

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 compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme.

Elliptic Curve Digital Signature Algorithm

In cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography. As with elliptic-curve cryptography in general, the bit size of the private key believed to be needed for ECDSA is about twice the size of the security level, in bits. For example, at a security level of 80 bits—meaning an attacker requires a maximum of about operations to find the private key—the size of an ECDSA private key would be 160 bits.

Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod p when p is a prime number. The order of a finite field is its number of elements, which is either a prime number or a prime power.

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