Elliptic Curve Public Key Cryptosystems (The Springer by Alfred J. Menezes

By Alfred J. Menezes

Elliptic curves were intensively studied in algebraic geometry and quantity conception. lately they've been utilized in devising effective algorithms for factoring integers and primality proving, and within the building of public key cryptosystems.
Elliptic Curve Public Key Cryptosystems offers an updated and self-contained therapy of elliptic curve-based public key cryptology. Elliptic curve cryptosystems probably offer identical safeguard to the present public key schemes, yet with shorter key lengths. Having brief key lengths skill smaller bandwidth and reminiscence necessities and will be a vital consider a few purposes, for instance the layout of shrewdpermanent card structures. The booklet examines numerous matters which come up within the safe and effective implementation of elliptic curve systems.
Elliptic Curve Public Key Cryptosystems is a helpful reference source for researchers in academia, govt and who're all for problems with facts safeguard. end result of the complete therapy, the ebook is usually appropriate to be used as a textual content for complex classes at the subject.

Show description

Read Online or Download Elliptic Curve Public Key Cryptosystems (The Springer International Series in Engineering and Computer Science) PDF

Similar cryptography books

Introduction to Cryptography

As a result of the speedy development of electronic conversation and digital info trade, details protection has turn into a very important factor in undefined, enterprise, and management. glossy cryptography offers crucial thoughts for securing info and retaining info. within the first half, this ebook covers the foremost suggestions of cryptography on an undergraduate point, from encryption and electronic signatures to cryptographic protocols.

Public Key Cryptography – PKC 2004: 7th International Workshop on Theory and Practice in Public Key Cryptography, Singapore, March 1-4, 2004. Proceedings

This publication constitutes the refereed court cases of the seventh overseas Workshop on concept and perform in Public Key Cryptography, PKC 2004, held in Singapore in March 2004. The 32 revised complete papers awarded have been rigorously reviewed and chosen from 106 submissions. All present concerns in public key cryptography are addressed starting from theoretical and mathematical foundations to a wide number of public key cryptosystems.

The Mathematics of Coding Theory, 1st Edition

This publication makes a really available creation to a crucial modern program of quantity thought, summary algebra, and chance. It includes quite a few computational examples all through, giving rookies the chance to use, perform, and cost their realizing of key recommendations. KEY themes assurance begins from scratch in treating likelihood, entropy, compression, Shannon¿s theorems, cyclic redundancy assessments, and error-correction.

Extra info for Elliptic Curve Public Key Cryptosystems (The Springer International Series in Engineering and Computer Science)

Sample text

There are several efficient polynomial time algorithms for finding the roots of a polynomial over F2mj for example, see [10]. 7 Notes The work of Waterhouse is based on Deuring's classic paper [32). Deuring considers two elliptic curves defined over Fq to be isomorphic over Fq if they are isomorphic, in our sense, over Fq. Some of Waterhouse's work was generalized by Ruck [133) to Jacobians of algebraic curves of genus 2 over finite fields. 6 is taken from [94). Jogarithm Problem There are many public-key cryptosystems whose security lies in the presumed intractability of the discrete logarithm problem in some group G.

1 Introduction Let (%) denote the usual Jacobi symbol. We also define (i) ~: if a == ±1 mod 8, if a· == 0 mod 2, = { -1, if a == ±3 mod 8. Waterhouse [152] (see also [137]) counted the number of isomorphism classes of elliptic curves defined over the finite field Fq by first determining which rings can occur as the endomorphism ring of some elliptic curve, and then counting the number of isomorphism classes of elliptic curves with a given endomorphism ring. He also proceeded to determine Nq(t), the number of isomorphism cla~ses of elliptic curves over Fq such that #E(Fq ) = q + 1 - t.

Type II: a3 is a cube, and Te(a4) f; O. Type III: a3 is a cube, and Te( a4) = O. Type I Curves We call a Type I curve with the coefficient of x being 0, a Type Ia curve. 11) Since a3 = a3/ u 3 and a3 is a non-cube, a3 is also a non-cube. Hence E2 is also a Type I curve. 11) in F2m. 9) has exactly 3 solutions. namely Ut,CIU}, and C2Ul. 10) has exactly one solution for each choice of u. 10) are 8 = 81,CI8},C281 respectively. 11), namely tl and tl +a3' Thus there are 6 admissible changes of variables which transform El to E 2 • Since the total number of admissible changes of variables is (q -1 )q2, the number of curves isomorphic to El is (q - 1)q2/6.

Download PDF sample

Rated 4.43 of 5 – based on 10 votes