guide to elliptic curve cryptography

Guide to Elliptic Curve Cryptography Darrel Hankerson Alfred Menezes Scott Vanstone Springer Guide to Elliptic Curve Cryptography Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo [...]... Signature Standard Elliptic Curve Cryptography Elliptic Curve Decision Diffie-Hellman Problem Elliptic Curve Diffie-Hellman Elliptic Curve Diffie-Hellman Problem Elliptic Curve Discrete Logarithm Problem Elliptic Curve Digital Signature Algorithm Elliptic Curve Integrated Encryption Scheme Elliptic Curve Korean Certificate-based Digital Signature Algorithm Elliptic Curve Menezes-Qu-Vanstone Extended Euclidean... subgroups of such elliptic curve groups can now be used to implement discrete logarithm systems We next illustrate the ideas behind elliptic curve cryptography by describing an elliptic curve analogue of the DL encryption scheme that was introduced in §1.2.2 Such elliptic curve systems, and also the elliptic curve analogue of the DSA signature scheme, are extensively studied in Chapter 4 Elliptic curve key... included these protocols in their security products The purpose of this chapter is to explain the advantages of public-key cryptography over traditional symmetric-key cryptography, and, in particular, to expound the virtues of elliptic curve cryptography The exposition is at an introductory level We provide more detailed treatments of the security and efficient implementation of elliptic curve systems in... Koblitz and Victor Miller independently proposed using elliptic curves to design public-key cryptographic systems Since then an abundance of research has been published on the security and efficient implementation of elliptic curve cryptography In the late 1990’s, elliptic curve systems started receiving commercial acceptance when accredited standards organizations specified elliptic curve protocols, and... statement of the fundamental goals of cryptography and a description of the essential differences between symmetric-key cryptography and public-key cryptography In §1.2, we review the RSA, discrete logarithm, and elliptic curve families of public-key systems These systems are compared in §1.3 in which we explain the potential benefits offered by elliptic curve cryptography A roadmap for the remainder... validation Generating a random elliptic curve over a prime field F p Verifying that an elliptic curve over F p was randomly generated Generating a random elliptic curve over a binary field F2m Verifying that an elliptic curve over F2m was randomly generated Generating a random elliptic curve over an OEF F pm Verifying that an elliptic curve over F pm was randomly generated Key... Finally, complete descriptions of the communications protocols and any cryptographic mechanisms deployed (except for secret keying information) are known to E The challenge to cryptographers is to design mechanisms to secure the communications in the face of such powerful adversaries Symmetric-key cryptography Cryptographic systems can be broadly divided into two kinds In symmetric-key schemes, depicted in... Public-key cryptography was conceived in 1976 by Whitfield Diffie and Martin Hellman The first practical realization followed in 1977 when Ron Rivest, Adi Shamir and Len Adleman proposed their now well-known RSA cryptosystem, in which security is based on the intractability of the integer factorization problem Elliptic curve cryptography (ECC) was discovered in 1985 by Neal Koblitz and Victor Miller Elliptic curve. .. parameters and Q is the elliptic curve discrete logarithm problem (ECDLP) Algorithm 1.12 Elliptic curve key pair generation I NPUT: Elliptic curve domain parameters ( p, E, P, n) O UTPUT: Public key Q and private key d 1 Select d ∈ R [1, n − 1] 2 Compute Q = d P 3 Return(Q, d) Elliptic curve encryption scheme We present the encryption and decryption procedures for the elliptic curve analogue of the basic... from M 2 Return(m) 1.3 Why elliptic curve cryptography? 15 1.3 Why elliptic curve cryptography? There are several criteria that need to be considered when selecting a family of publickey schemes for a specific application The principal ones are: 1 Functionality Does the public-key family provide the desired capabilities? 2 Security What assurances are available that the protocols are secure? 3 Performance . Guide to Elliptic Curve Cryptography Darrel Hankerson Alfred Menezes Scott Vanstone Springer Guide to Elliptic Curve Cryptography Springer New York Berlin Heidelberg Hong. Standard ECC Elliptic Curve Cryptography ECDDHP Elliptic Curve Decision Diffie-Hellman Problem ECDH Elliptic Curve Diffie-Hellman ECDHP Elliptic Curve Diffie-Hellman Problem ECDLP Elliptic Curve Discrete. Overview 1 1.1 Cryptographybasics 2 1.2 Public-keycryptography 6 1.2.1 RSAsystems 6 1.2.2 Discretelogarithmsystems 8 1.2.3 Elliptic curve systems 11 1.3 Why elliptic curve cryptography? . . .