Elliptic Curves and Cryptography
نویسندگان
چکیده
Elliptic curves also figured prominently in the recent proof of Fermat's Last Theorem by Andrew Wiles. Originally pursued for purely aesthetic reasons, elliptic curves have recently been utilized in devising algorithms for factoring integers, primality proving, and in public-key cryptography. In this article, we aim to give the reader an introduction to elliptic curve cryptosystems, and to demonstrate why these systems provide relatively small block sizes, high-speed software and hardware implementations, and offer the highest strength-per-key-bit of any known public-key scheme.
منابع مشابه
Efficient elliptic curve cryptosystems
Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...
متن کاملThe new protocol blind digital signature based on the discrete logarithm problem on elliptic curve
In recent years it has been trying that with regard to the question of computational complexity of discrete logarithm more strength and less in the elliptic curve than other hard issues, applications such as elliptic curve cryptography, a blind digital signature method, other methods such as encryption replacement DLP. In this paper, a new blind digital signature scheme based on elliptic curve...
متن کاملElliptic Curves and Cryptography
This paper begins by discussing the foundations of the study of elliptic curves and how a the points on an elliptic curve form an additive group. We then explore some of the interesting features of elliptic curves, including the fact that elliptic curves are complex tori. At the end we briefly discuss how elliptic curves can be used in cryptography.
متن کاملApplications of Elliptic Curves in Cryptography
This paper will examine the role of elliptic curves in the field of cryptography. The applicability of an analogous discrete logarithm problem to elliptic curve groups provides a basis for the security of elliptic curves. Two cryptographic protocols which implement elliptic curves are examined as well as two popular methods to solve the elliptic curve discrete logarithm problem. Finally, a comp...
متن کاملApplication of Elliptic Curves Cryptography In Wireless Communications Security
This paper provides an overview of elliptic curves and their use in cryptography. The focus of the paper is on the performance advantages obtained in the wireless environments by using elliptic curve cryptography instead of traditional cryptosystems such as RSA. Specific applications to secure messaging and identity-based encryption are also discussed. keywords: elliptic curves, wireless, Digit...
متن کاملProvably secure and efficient identity-based key agreement protocol for independent PKGs using ECC
Key agreement protocols are essential for secure communications in open and distributed environments. Recently, identity-based key agreement protocols have been increasingly researched because of the simplicity of public key management. The basic idea behind an identity-based cryptosystem is that a public key is the identity (an arbitrary string) of a user, and the corresponding private key is ...
متن کامل