Elliptic Curve Cryptography
Abstract This paper gives an introduction to elliptic curve cryptography (ECC) and how it is used in the implementation of digital signature (ECDSA) and key agreement (ECDH) Algorithms. The paper discusses the implementation of ECC on two finite fields, prime field and binary field. It also gives an overview of ECC implementation on different coordinate systems called the projective coordinate systems. The paper also discusses the basics of prime and binary field arithmetic. This paper also discusses why ECC is a better option than RSA in modern day systems. This paper also discusses why ECC 's unique properties make it especially well suited to smart card applications.
Index TermsElliptic Curve Cryptography, Smart Cards, Discrete Logarithm problem
I. INTRODUCTION
Over the past 30 years, public key cryptography has become a mainstay for secure communications over the Internet and throughout many other forms of communications. It provides the foundation for both key management and digital signatures. In key management, public key cryptography is used to distribute the secret keys used in other cryptographic algorithms (e.g. DES). For digital signatures, public key cryptography is used to authenticate the origin of data and protect the integrity of that data. For the past 20 years, Internet communications have been secured by the first generation of public key cryptographic algorithms developed in the mid-1970 's. Notably, they form the basis for key management and authentication for IP encryption (IKE/IPSEC), web traffic (SSL/TLS) and secure electronic mail.
In their day these public key techniques revolutionized cryptography. Over the last twenty years however, new techniques have been developed which offer both better performance and higher security than these first generation public key techniques. The best assured group of new public key techniques is built on the arithmetic of elliptic curves. Elliptic Curve Cryptography (ECC) is one of best public
Index TermsElliptic Curve Cryptography, Smart Cards, Discrete Logarithm problem
I. INTRODUCTION
Over the past 30 years, public key cryptography has become a mainstay for secure communications over the Internet and throughout many other forms of communications. It provides the foundation for both key management and digital signatures. In key management, public key cryptography is used to distribute the secret keys used in other cryptographic algorithms (e.g. DES). For digital signatures, public key cryptography is used to authenticate the origin of data and protect the integrity of that data. For the past 20 years, Internet communications have been secured by the first generation of public key cryptographic algorithms developed in the mid-1970 's. Notably, they form the basis for key management and authentication for IP encryption (IKE/IPSEC), web traffic (SSL/TLS) and secure electronic mail.
In their day these public key techniques revolutionized cryptography. Over the last twenty years however, new techniques have been developed which offer both better performance and higher security than these first generation public key techniques. The best assured group of new public key techniques is built on the arithmetic of elliptic curves. Elliptic Curve Cryptography (ECC) is one of best public
References: [1] http://www.wikipedia.org [2] Certicom Corp. Current Public-Key Cryptographic Systems, April 1997. http://www.certicom.com/research/wecc2.html. [3] K. Araki, S. Miura, and T. Satoh. Overview of elliptic curve cryptography. In International Workshop on Practice and Theory in Public Key Cryptography, pages 1-14, 1998. [4]Elliptic curve cryptosystems on smart cards Elsayed Mohammed, A. E. Emarah and 0. El-Shennawy, Senior Member IEEE [5] A.J. Menezes. Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers, 1993. [6] Michael Rosing. Implementing Elliptic Curve Cryptography. Manning Publications, first edition, 1999. [7] Cryptography and Network security, William Stallings, Prentice Hall, Fourth Edition