Elliptic curve cryptography (ECC) was introduced by Victor Miller and Neal Koblitz in 1985. ECC proposed as an alternative to established public-key systems such as DSA and RSA, have recently gained a lot attention in industry and academia. The main reason for the attractiveness of ECC is the fact that there is no sub-exponential algorithm known to solve the discrete logarithm problem on a properly chosen elliptic curve. This means that significantly smaller parameters can be used in ECC than in other competitive systems such RSA and DSA, but with equivalent levels of security. Some benefits of having smaller key sizes include faster computations, and reductions in processing power, storage space and bandwidth. This makes ECC ideal for constrained environments such as pagers, PDAs, cellular phones and smart cards. The implementation of ECC, on the other hand, requires several choices such as the type of the underlying finite field, algorithms for implementing the finite field arithmetic and so on. In this paper we give we presen an selective overview of the main methods.

The Elliptic Curve Cryptosystem (ECC) is an emerging alternative for traditional Public-Key Cryptosystem like RSA, DSA and DH. It provides the highest strength-per-bit of any cryptosystem known today with smaller key sizes resulting in faster computations, lower power consumption and memory. It also provides a methodology for obtaining high-speed, efficient and scalable implementation of protocols for authentication and key agreement. This paper provides an introduction to Elliptic Curves and how they are used to create a secure and powerful cryptosystem. It provides an overview of the three hard mathematical problems that provide the basis for the security of public key cryptosystems used today: the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problem (ECDLP). It explains the proposed protocol which is improved to reduce the storage requirements for establishing a shared secret key between two parties, to sign and verify a document and to establish a mutual authentication between two parties. The result of implementation is also discussed.

In recent years, several studies have been conducted on software implementation of elliptic curve cryptosystems (ECC). In this note we have collected several details of reported software implementations of these cryptosystems. For each implementation considered, we include, if available, the platform used, and running times for: nite eld operations, scalar multiplications, and protocols such as the ECDSA. This compilation is organized in ve sections: performance of ECC over F 2 m , performance of ECC over F p , performance of ECC over F p m , implementations comparing F 2 m and F p , and implementations comparing ECC with other public-key systems such as RSA and DL. 1 Performance of ECC over F 2 m \Fast key exchange with elliptic curve system" [22] { Author: R. Schroeppel et al, 1995 { Platform: SPARC 25MHz; language: C { Representation: Trinomial basis for F 2 155 { Curves: Random curves { Timings: m Sqr. (sec) Mul. (sec) Inv. AIA 1 (sec) kP (msec) 155 8 112 280 92 ...

In this paper we propose a secure protocol for authenticated key agreement based on Diffie-Hellman key agreement, which works in an elliptic curve group. We also present a simpler authenticated key agreement protocol than the proposed one and a multiple key agreement protocol which enables the participants to share two or more keys in one execution of the protocol. We prove that our protocols meet the security attributes under the assumption that the elliptic curve discrete logarithm problem is secure. Key Words: Protocols, authenticated key agreement, elliptic curves. 1.

Anonymity is a very important security feature in addition to authentication and key agreement features in communication protocols. In this paper, we propose two authentication and key agreement (AKA) protocols: the AKA protocol with user anonymity (UAP) and the AKA protocol with user and server anonymity (USAP). The proposed protocols have the following advantages: first of all, they preserve anonymity, which is a security feature that was ignored in most of the previously proposed AKA protocols; secondly, they exploit the difference in capabilities between resource constrained clients and highly resourceful servers and thus are suitable for wireless applications; thirdly, they resist known attacks; and finally, they perform better in terms of the number of messages and bits exchanged and computing time as compared to the previously proposed AKA protocols. For example, USAP preserves user and server anonymity, exchanges 3 messages with 1920 bits in total, and requires only 280 msec of processing time on the user side when implemented on Mitsubishis M16C microprocessor. Similarly, the UAP is scalable, preserves user anonymity, requires 440 msec, and exchanges 2560 bits.

Abstract—In this paper the authors propose a protocol, which uses Elliptic Curve Cryptography (ECC) based on the ElGamal’s algorithm, for sending small amounts of data via an authentication server. The innovation of this approach is that there is no need for a symmetric algorithm or a safe communication channel such as SSL. The reason that ECC has been chosen instead of RSA is that it provides a methodology for obtaining high-speed implementations of authentication protocols and encrypted mail techniques while using fewer bits for the keys. This means that ECC systems require smaller chip size and less power consumption. The proposed protocol has been implemented in Java to analyse its features and vulnerabilities in the real world. Keywords—Elliptic Curve Cryptography (ECC), ElGamal, and authentication protocol. I. ELLIPTIC CURVE CRYPTOGRAPHY (ECC)

In recent years, the elliptic curve cryptosystems (ECC) have received attention due to their increased security with smaller key size which brings the advantage of less storage area and less bandwidth. Elliptic curve cryptography provides a methodology for obtaining high-speed, efficient, and scalable implementations of network security protocols. In addition low power consumption and code size reductions are the other benefits of the ECC-based security architectures. In this thesis, we mainly concentrate on public key authentication and key agree-ment protocols. After discussing several well-known protocols, we propose an authentication and key agreement protocol for wireless communication based on the elliptic curve cryptographic techniques. The proposed protocol requires significantly less bandwidth than the Aziz-Diffie and Beller-Chang-Yacobi protocols, and furthermore, it has lower computational burden and storage requirements on the user side. Additionally,we present an end-to-end mobile user security protocol. The protocol is an improved version of the previous one in terms of security and interoperability. The achievement on the protocol goals and the complete security analysis are also

An important and challenging problem is that of tracing DOS/DDOS attack source. Among many IP Traceback schemes, a recent development is DGT (Directed Geographical Traceback). Though multidirectional two dimensional DGT schemes are available, ξξξin the real scenario, three dimensional, Multidirectional DGT has potential applications. The direction ratio algorithm[DRA] has the limitation of the impossibility of ensuring sufficient unused space in the packet header for the complete DRL (Direction Ratio List) especially when the length of the path is not known apriori. In this paper that limitation is overcome using DRSA(Direction Ratio Sampling Algorithm) which works well for Three dimensional, Multi-Directional, Geographical IP traceback. This approach enables the attack path reconstruction easily possible. In conclusion, DRSA is a robust scheme of attack path reconstruction in geographical traceback.

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